Stochastics Books
Springer International Publishing AG Correlated Random Systems: Five Different Methods: CIRM Jean-MorletChair, Spring 2013
Book SynopsisThis volume presents five different methods recently developed to tackle the large scale behavior of highly correlated random systems, such as spin glasses, random polymers, local times and loop soups and random matrices. These methods, presented in a series of lectures delivered within the Jean-Morlet initiative (Spring 2013), play a fundamental role in the current development of probability theory and statistical mechanics. The lectures were: Random Polymers by E. Bolthausen, Spontaneous Replica Symmetry Breaking and Interpolation Methods by F. Guerra, Derrida's Random Energy Models by N. Kistler, Isomorphism Theorems by J. Rosen and Spectral Properties of Wigner Matrices by B. Schlein.This book is the first in a co-edition between the Jean-Morlet Chair at CIRM and the Springer Lecture Notes in Mathematics which aims to collect together courses and lectures on cutting-edge subjects given during the term of the Jean-Morlet Chair, as well as new material produced in its wake. It is targeted at researchers, in particular PhD students and postdocs, working in probability theory and statistical physics.Table of Contents1 Random Polymers.- 2 Spontaneous replica symmetry breaking and interpolation methods for complex statistical mechanics systems.- 3 Derrida’s random energy models: from spin glasses to the extremes of correlated random fields.- 4 Isomorphism Theorems: Markov processes, Gaussian processes and beyond.- 5 Spectral properties of Wigner matrices.
£38.94
Gabler Grundlagen statistischer Wahrscheinlichkeiten: Kombinationen, Wahrscheinlichkeiten, Binomial- und Normalverteilung, Konfidenzintervalle, Hypothesentests
Book SynopsisEndlich verstehen Sie die ökonomischen Anwendungsmöglichkeiten und Funktionsweisen statistischer Wahrscheinlichkeiten im Betrieb! Dieses Buch vermittelt Ihnen die grundlegenden Verfahren der Wahrscheinlichkeitsrechnung als auch der Wahrscheinlichkeitsverteilungen und zeigt Ihnen deren praktische Anwendung in Betrieb und Ökonomie. Beispiele und Fragen mit Musterlösungen dienen dem weiteren Verständnis.Table of ContentsGrundlagen statistischer Wahrscheinlichkeiten in der Betriebswirtschaft: Grundbegriffe der Wahrscheinlichkeitsrechnung Diskrete Wahrscheinlichkeitsverteilungen - Binomial- und Hypergeometrische Verteilung Stetige Wahrscheinlichkeitsverteilung - Normalverteilung Intervallschätzung Notwendiger Stichprobenumfang Wahlforschung Hypothesentestverfahren Tabelle der Standardnormalverteilung Mathematische Grundlagen der induktiven Statistik Lösungen
£27.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Einführung in Die Statistik für Sozial- Und Erziehungs-wissenschaftler
Book SynopsisIn den empirischen Sozialwissenschaften dienen die Methoden und Techniken der Statistik der Auswertung von Ergebnissen empirischer Untersuchungen und ermöglicht so die Beschreibung der quantitiativen Eigenschaften einer beobachteten und vollständig erfassten Gruppe. Das vorliegende Buch beschäftigt sich nahezu ausschließlich mit deskriptiver Statistik, welche sich mit der Aufbereitung und Beschreibung von Datenmengen und deren Verteilung befasst. Nach einer ausführlichen und grundlegenden Einführung in das Thema werden die wichtigsten Häufigkeitsverteilungen sowie die Maßzahlen zu deren Beschreibung dargestellt. Mit der linearen Einfachregression wird zuletzt der lineare funktionale Zusammenhang zweier Variabler erläutert. Zu jedem Kapitel gibt es Beispiele, Übungsaufgaben und eine Zusammenfassung. Im Anhang befinden sich mehrere Klausuren mit Lösungen, die in den letzten Jahren an der TU Dresden benutzt wurden.Table of Contents1 Grundlagen.- 1.1 Geisteswissenschaften und empirische Wissenschaften heute.- 1.2 Grundmethoden der empirischen Wissenschaften.- 1.2.1 Untersuchungsformen.- 1.2.2 Datenerhebungstechniken.- 1.2.3 Auswahlverfahren.- 1.3 Ablauf empirischer Sozialforschung: Der Forschungsprozess.- 1.3.1 Auswahl des Forschungsgegenstandes.- 1.3.2 Theoriebildung.- 1.3.3 Planung der Untersuchung.- 1.3.4 Durchführung der Untersuchung (Datenerhebung).- 1.3.5 Beschreibung und Zusammenfassung der Ergebnisse.- 1.3.6 Verallgemeinerung der Ergebnisse und Publikation.- 1.4 Einführung in die Forschungsstatistik.- 1.4.1 Statistische Gesetzmäßigkeiten.- 1.4.2 Grundlegende statistische Begriffe.- 1.4.3 Statistische Symbole.- 1.5 Begriff des Messens und der Messskalen.- 1.5.1 Der Begriff des Messens.- 1.5.2 Die Messniveaus.- 1.5.3 Die Bedeutung der Messniveaus für die Statistik.- 1.5.4 Gütekriterien der Messung.- Aufgaben.- 2 Empirische Häufigkeitsverteilungen.- 2.1 Häufigkeit und Verteilung.- 2.1.1 Das Aufstellen einer Häufigkeitstabelle.- 2.1.2 Absolute, relative und prozentuale Häufigkeiten.- 2.1.3 Die Häufigkeitsfunktion.- 2.1.4 Die Empirische Verteilungsfunktion.- 2.2 In Klassen eingeteilte Merkmale.- 2.2.1 Das Einteilen der Messwerte in Klassen.- 2.2.2 Aufstellen der Klassenhäufigkeiten.- 2.2.3 Offene Klassen.- 2.2.4 Exakte Klassengrenzen.- 2.2.5 Repräsentation einer Klasse durch die K1assenmitte.- 2.2.6 Informationsverlust durch Klasseneinteilung.- 2.3 Graphische Darstellungen von Häufigkeitsverteilungen.- 2.3.1 Das Stab-oder Balkendiagramm.- 2.3.2 Das Kreisdiagramm.- 2.3.3 Das Histogramm.- 2.3.4 Das Polygon.- 2.3.5 Typische Fonnen spezieller Verteilungen.- 2.4 Erkennen von Fehlinformation in statistischen Analysen.- 3 Maßzahlen eindimensionaler Verteilungen.- 3.1 Lageparameter.- 3.1.1 Das arithmetische Mittel.- 3.1.2 Der Median.- 3.1.3 Der Modus.- 3.1.4 Relative Positionen.- 3.1.5 Zulässige und optimale Lageparameter der einzelnen Messniveaus.- 3.2 Dispersionsparameter.- 3.2.1 Spannweite.- 3.2.2 Der (mittlere) Quartilabstand.- 3.2.3 Standardabweichung und Varianz.- 3.2.4 Der Variationskoeffizient zum Vergleich mehrerer Stichproben.- 3.2.5 Die Zusammenfassung von Varianzen.- 3.2.6 Gesamtvarianz, systematische Varianz und Fehlervarianz.- 3.2.7 Die Summe der quadratischen Abweichungen.- Aufgaben.- 4 Maßzahlen zweidimensionaler Verteilungen.- 4.1 Vorbemerkungen.- 4.1.1 Linearität.- 4.1.2 Die gemeinsame Verteilung.- 4.1.3 Ein einfaches Beispiel zur Darstellung bivariater Verteilungen.- 4.2 Korrelation.- 4.2.1 Intervallniveau.- 4.2.2 Ordinalniveau.- 4.3 Nomina1niveau.- 4.3.1 Tau (Goodman und Kruskal).- 4.3.2 Lambda.- 4.3.3 Kontingenzkoeffizient.- 4.3.4 Phi.- 4.3.5 Cramer’s V.- 4.4 Interpretation.- 5 Die lineare Einfachregression.- 5.1 Anpassen von Kurven.- 5.2 Vorhersage bei korrelierten Variablen.- 5.3 Methode der kleinsten Quadrate.- 5.3.1 Berechnung der Regressionsgeraden Gy/x.- 5.3.2 Berechnung der Regressionsgeraden Gx/y.- 5.4 Regressionskoeffizient, Korrelationskoeffizient und Varianz.- 5.5 Der Korrelationskoeffizient als Maß für die Güte der Regression.- 5.5.1 Die Varianz um die Regressionsgerade Sy/x2.- 5.5.2 Die Varianz auf der Regressionsgeraden $$ s_{\tilde y}^2 $$.- 5.6 Berechnung zweier Beispielaufgaben.- 5.6.1 Beispiel 1.- 5.6.2 Beispiel 2.- Weiterführende Literatur.- Anhang 1 Probeklausuren.- Anhang 2 Lösungen zu den Probeklausuren.
£29.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Probability in Banach Spaces: Isoperimetry and
Book SynopsisIsoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.Trade ReviewThis book gives an excellent, almost complete account of the whole subject of probability in Banach spaces, a branch of probability theory that has undergone vigorous development... There is no doubt in the reviewer's mind that this book [has] become a classic. MathSciNetAs the authors state, "this book tries to present some of the main aspects of the theory of probability in Banach spaces, from the foundation of the topic to the latest developments and current research questions''. The authors have succeeded admirably… This very comprehensive book develops a wide variety of the methods existing … in probability in Banach spaces. … It [has] become an event for mathematicians… Zentralblatt MATHTable of ContentsNotation.- 0. Isoperimetric Background and Generalities.- 1. Isoperimetric Inequalities and the Concentration of Measure Phenomenon.- 2. Generalities on Banach Space Valued Random Variables and Random Processes.- I. Banach Space Valued Random Variables and Their Strong Limiting Properties.- 3. Gaussian Random Variables.- 4. Rademacher Averages.- 5. Stable Random Variables.- 6 Sums of Independent Random Variables.- 7. The Strong Law of Large Numbers.- 8. The Law of the Iterated Logarithm.- II. Tightness of Vector Valued Random Variables and Regularity of Random Processes.- 9. Type and Cotype of Banach Spaces.- 10. The Central Limit Theorem.- 11. Regularity of Random Processes.- 12. Regularity of Gaussian and Stable Processes.- 13. Stationary Processes and Random Fourier Series.- 14. Empirical Process Methods in Probability in Banach Spaces.- 15. Applications to Banach Space Theory.- References.
£44.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Derivation and Martingales
Book SynopsisIn Part I of this report the pointwise derivation of scalar set functions is investigated, first along the lines of R. DE POSSEL (abstract derivation basis) and A. P. MORSE (blankets); later certain concrete situations (e. g. , the interval basis) are studied. The principal tool is a Vitali property, whose precise form depends on the derivation property studied. The "halo" (defined at the beginning of Part I, Ch. IV) properties can serve to establish a Vitali property, or sometimes produce directly a derivation property. The main results established are the theorem of JESSEN-MARCINKIEWICZ-ZYGMUND (Part I, Ch. V) and the theorem of A. P. MORSE on the universal derivability of star blankets (Ch. VI) . . In Part II, points are at first discarded; the setting is somatic. It opens by treating an increasing stochastic basis with directed index sets (Th. I. 3) on which premartingales, semimartingales and martingales are defined. Convergence theorems, due largely to K. KRICKEBERG, are obtained using various types of convergence: stochastic, in the mean, in Lp-spaces, in ORLICZ spaces, and according to the order relation. We may mention in particular Th. II. 4. 7 on the stochastic convergence of a submartingale of bounded variation. To each theorem for martingales and semi-martingales there corresponds a theorem in the atomic case in the theory of cell (abstract interval) functions. The derivates concerned are global. Finally, in Ch.Table of ContentsI Pointwise Derivation.- I: Derivation Bases.- 1. Setting and general notation.- 2. dePossel’s derivation basis.- 3. Examples of bases.- 4. Pretopological notions.- 5. Comparison lemmas.- II: Derivation Theorems for ?-additive Set Functions under Assumptions of the Vitali Type.- 1. The individual Vitali assumption.- 2. The individual full derivation theorem for Radon or ?-fmite ?-integrals.- 3. The individual full derivation theorem for Radon measures.- 4. Class derivation theorems.- 5. Relation to Younovitch’s derivation theorem.- 6. The strong Vitali property.- 7. Half-regular and regular branches of a derivation basis.- III: The Converse Problem I: Covering Properties Deduced from Derivation Properties of ?-additive Set Functions.- 1. dePossel’s equivalence theorem.- 2. A necessary and sufficient condition for a weak derivation basis to derive a ?-finite ?-measure (Radon measure) ?.- 3. Younovitch’s equivalence theorem.- 4. A converse theorem for bases deriving the ?(q)-functions, q ? 1.- IV: Halo Assumptions in Derivation Theory. Converse Problem II.- 1. A. P. Morse’s halo properties.- 2. Abstract version of the strong Vitali theorem modelled after Banach.- 3. Abstract version of the strong Vitali theorem modelled after Carathéodory.- 4. Weak halo evanescence condition.- 5. Further criteria for the validity of the Density Theorem involving the weak halo.- 6. An individual derivability condition of Busemann-Feller type.- 7. The weak halo property in general bases.- 8. Product invariance of a weak halo property.- V: The Interval Basis. The Theorem of Jessen-Marcin-Kiewicz-Zygmund.- 1. The interval basis as a weak derivation basis.- 2. Theorem of Jessen-Marcinkiewicz-Zygmund.- 3. Properties of the halo function as consequences of derivation properties.- 4. Saks’ counterexample.- 5. The parallelepipedon basis.- 6. Saks’ “rarity” theorem.- VI: A. P. Morse’s Blankets.- 1. Nets.- 2. Hives.- 3. Fundamental covering theorems.- 4. Star blankets.- II Martingales and Cell Functions.- I: Theory without an Intervening Measure.- 1. Additive functions.- 2. ?-additive functions.- 3. Premartingales, semi-martingales, and martingales.- 4. Ordered space of martingales of basis(??).- 5. Integrals of premartingales.- 6. Martingales and additive functions.- 7. ?-additive martingales.- 8. Induced martingales.- 9. Premartingales and cell functions.- 10. Integrals of cell functions.- 11. Convergence theorems for martingales of bounded variation when ? is a measure algebra.- II: Theory in a Measure Space without Vitali Conditions.- 1. Preliminaries.- 2. Absolutely continuous and singular premartingales.- 3. Stochastic processes.- 4. Stochastic convergence.- 5. Mean convergence of order 1.- 6. Convergence in Orlicz spaces.- 7. Cell functions.- III: Theory in a Measure Space with Vitali Conditions.- 1. Preliminaries and definitions.- 2. Vitali conditions.- 3. Order convergence of martingales.- 4. Necessity of the Vitali conditions.- 5. Order convergence of submartingales.- 6. Order convergence of cell functions.- IV: Applications.- 1. Pointwise setting.- 2. Specifically pointwise concepts and results. Convergence almost everywhere.- 3. Martingales in the classical sense.- 4. Product spaces.- 5. The Radon- Nikodym integrand defined as a derivate.- 6. Representation of the spaces Lx as spaces of cell functions.- 7. Pointwise derivation of cell functions.- 8. Examples of concrete cell bases.- 9. Stochastic bases on a group.- Complements.- 1°. Derivation of vector-valued integrals.- 2°. Functional derivatives.- 3°. Topologies generated by measures.- 4°. Vitali’s theorem for invariant measures.- 5°. Global derivatives in locally compact topological groups..- 6°. Submartingales with decreasing stochastic bases.- 7°. Vector-valued martingales and derivation.- 9°. Derivation of measures.
£42.74
Springer Random Processes with Independent Increments
Book SynopsisOne SCI\'ice mathematics bas rendered the 'Et moi, ...si j'avait su comment en revcnir. je n'y serais point aile: human race. It bas put common sc:nsc back where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Hcavisidc Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly. all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. :; 'One service logic has rendered com- puter science .. :; 'One service category theory has rendered mathematics .. :. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.Table of Contents0. Preliminary Informationh.- 0.1 Probability Space.- 0.2 Random Functions and Processes.- 0.3 Conditional Probabilities.- 0.4 Independence.- 1. Sums of Independent Random Variables.- 1.1 Main Inequalities.- 1.2 Renewal Scheme.- 1.3 Random Walks. Recurrence.- 1.4 Distribution of Ladder Functions.- 2. General Processes with Independent Increments (Random Measures).- 2.1 Nonnegative Random Measures with Independent Values (r.m.i.v.).- 2.2 Random Measures with Alternating Signs.- 2.3 Stochastic Integrals and Countably Additive r.m.i.v.- 2.4 Random Linear Functional and Generalized Functions.- 3. Processes with Independent Increments. General Properties.- 3.1 Decomposition of a Process. Properties of Sample Functions.- 3.2 Stochastically Continuous Processes.- 3.3 Properties of Sample Functions.- 3.4 Locally Homogeneous Processes with Independent Increments.- 4. Homogeneous Processes.- 4.1 General Properties.- 4.2 Additive Functionals.- 4.3 Composed Poisson Process.- 4.4 Homogeneous Processes in R.- 5. Multiplicative Processes.- 5.1 Definition and General Properties.- 5.2 Multiplicative Processes in Abelian Groups.- 5.3 Stochastic Semigroups of Linear Operators in Rd.- Notes.- References.
£42.74
World Scientific Publishing Co Pte Ltd First Look At Stochastic Processes, A
Book SynopsisThis textbook introduces the theory of stochastic processes, that is, randomness which proceeds in time. Using concrete examples like repeated gambling and jumping frogs, it presents fundamental mathematical results through simple, clear, logical theorems and examples. It covers in detail such essential material as Markov chain recurrence criteria, the Markov chain convergence theorem, and optional stopping theorems for martingales. The final chapter provides a brief introduction to Brownian motion, Markov processes in continuous time and space, Poisson processes, and renewal theory.Interspersed throughout are applications to such topics as gambler's ruin probabilities, random walks on graphs, sequence waiting times, branching processes, stock option pricing, and Markov Chain Monte Carlo (MCMC) algorithms.The focus is always on making the theory as well-motivated and accessible as possible, to allow students and readers to learn this fascinating subject as easily and painlessly as possible.
£999.99
The University of Chicago Press Dimension Theory in Dynamical Systems
Book SynopsisThe principles of symmetry and self-symmetry are expressed in fractals, the subject of study in dimension theory. This book introduces an area of research which has recently appeared in the interface between dimension theory and the theory of dynamical systems, focusing on invariant fractals.
£30.40
Springer New York Probability Theory
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£49.49
Springer-Verlag New York Inc. Information Theory and Network Coding Information
Book SynopsisThis book is an evolution from my book A First Course in Information Theory published in 2002 when network coding was still at its infancy.Trade ReviewFrom the reviews: "This book could serve as a reference in the general area of information theory and would be of interest to electrical engineers, computer engineers, or computer scientists with an interest in information theory. Each chapter has an appropriate problem set at the end and a brief paragraph that provides insight into the historical significance of the material covered therein. … Summing Up: Recommended. Upper-division undergraduate through professional collections." (J. Beidler, Choice, Vol. 46 (9), May, 2009) "The book consisting of 21 chapters is divided into two parts. Part I, Components of Information Theory … . Part II Fundamentals of Network Coding … . A comprehensive instructor’s manual is available. This is a well planned comprehensive book on the subject. The writing style of the author is quite reader friendly. … it is a welcome addition to the subject and will be very useful to students as well as to the researchers in the field." (Arjun K. Gupta, Zentralblatt MATH, Vol. 1154, 2009)Table of ContentsThe Science of Information.- The Science of Information.- Fundamentals of Network Coding.- Information Measures.- Information Measures.- Zero-Error Data Compression.- Weak Typicality.- Strong Typicality.- Discrete Memoryless Channels.- Rate-Distortion Theory.- The Blahut–Arimoto Algorithms.- Differential Entropy.- Continuous-Valued Channels.- Markov Structures.- Information Inequalities.- Shannon-Type Inequalities.- Beyond Shannon-Type Inequalities.- Entropy and Groups.- Fundamentals of Network Coding.- The Max-Flow Bound.- Single-Source Linear Network Coding: Acyclic Networks.- Single-Source Linear Network Coding: Cyclic Networks.- Multi-source Network Coding.
£71.99
Springer New York Probability and Stochastics
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£999.99
Springer New York Bayesian Forecasting and Dynamic Models Springer Series in Statistics
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£113.99
Springer New York Modeling Survival Data Extending the Cox Model Statistics for Biology and Health
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£161.99
John Wiley & Sons Inc LQ Dynamic Optimization and Differential Games
Book SynopsisLinear Quadratic Differential Games is an assessment of the state of the art in its field and modern book on linear-quadratic game theory, one of the most commonly used tools for modelling and analysing strategic decision making problems in economics and management.Table of ContentsPreface. Notation and symbols. 1 Introduction. 1.1 Historical perspective. 1.2 How to use this book. 1.3 Outline of this book. 1.4 Notes and references. 2 Linear algebra. 2.1 Basic concepts in linear algebra. 2.2 Eigenvalues and eigenvectors. 2.3 Complex eigenvalues. 2.4 Cayley–Hamilton theorem. 2.5 Invariant subspaces and Jordan canonical form. 2.6 Semi-definite matrices. 2.7 Algebraic Riccati equations. 2.8 Notes and references. 2.9 Exercises. 2.10 Appendix. 3 Dynamical systems. 3.1 Description of linear dynamical systems. 3.2 Existence–uniqueness results for differential equations. 3.2.1 General case. 3.2.2 Control theoretic extensions. 3.3 Stability theory: general case. 3.4 Stability theory of planar systems. 3.5 Geometric concepts. 3.6 Performance specifications. 3.7 Examples of differential games. 3.8 Information, commitment and strategies. 3.9 Notes and references. 3.10 Exercises. 3.11 Appendix. 4 Optimization techniques. 4.1 Optimization of functions. 4.2 The Euler–Lagrange equation. 4.3 Pontryagin’s maximum principle. 4.4 Dynamic programming principle. 4.5 Solving optimal control problems. 4.6 Notes and references. 4.7 Exercises. 4.8 Appendix. 5 Regular linear quadratic optimal control. 5.1 Problem statement. 5.2 Finite-planning horizon. 5.3 Riccati differential equations. 5.4 Infinite-planning horizon. 5.5 Convergence results. 5.6 Notes and references. 5.7 Exercises. 5.8 Appendix. 6 Cooperative games. 6.1 Pareto solutions. 6.2 Bargaining concepts. 6.3 Nash bargaining solution. 6.4 Numerical solution. 6.5 Notes and references. 6.6 Exercises. 6.7 Appendix. 7 Non-cooperative open-loop information games. 7.1 Introduction. 7.2 Finite-planning horizon. 7.3 Open-loop Nash algebraic Riccati equations. 7.4 Infinite-planning horizon. 7.5 Computational aspects and illustrative examples. 7.6 Convergence results. 7.7 Scalar case. 7.8 Economics examples. 7.8.1 A simple government debt stabilization game. 7.8.2 A game on dynamic duopolistic competition. 7.9 Notes and references. 7.10 Exercises. 7.11 Appendix. 8 Non-cooperative feedback information games. 8.1 Introduction. 8.2 Finite-planning horizon. 8.3 Infinite-planning horizon. 8.4 Two-player scalar case. 8.5 Computational aspects. 8.5.1 Preliminaries. 8.5.2 A scalar numerical algorithm: the two-player case. 8.5.3 The N-player scalar case. 8.6 Convergence results for the two-player scalar case. 8.7 Notes and references. 8.8 Exercises. 8.9 Appendix. 9 Uncertain non-cooperative feedback information games. 9.1 Stochastic approach. 9.2 Deterministic approach: introduction. 9.3 The one-player case. 9.4 The one-player scalar case. 9.5 The two-player case. 9.6 A fishery management game. 9.7 A scalar numerical algorithm. 9.8 Stochastic interpretation. 9.9 Notes and references. 9.10 Exercises. 9.11 Appendix. References. Index.
£101.66
John Wiley & Sons Inc Modeling Random Processes for Engineers and
Book SynopsisModeling Random Processes for Engineers and Managers provides students with a gentle introduction to stochastic processes, emphasizing full explanations and many examples rather than formal mathematical theorems and proofs. The text offers an accessible entry into a very useful and versatile set of tools for dealing with uncertainty and variation. Many practical examples of models, as well as complete explanations of the thought process required to create them, motivate the presentation of the computational methods. In addition, the text contains a previously unpublished computational approach to solving many of the equations that occur in Markov processes. Modeling Random Processes is intended to serve as an introduction, but more advanced students can use the case studies and problems to expand their understanding of practical uses of the theory.Table of ContentsPreface ix 1 Probability Review 1 1.1 Interpreting and Using Probabilities 2 1.2 Sample Spaces and Events 3 1.3 Probability 4 1.4 Random Variables 6 1.5 Probability Distributions 6 1.6 Joint, Marginal, and Conditional Distributions 11 1.7 Expectation 14 1.8 Variance and Other Moments 16 1.9 The Law of Total Probability 18 1.10 Discrete Probability Distributions 20 1.11 Continuous Probability Distributions 23 1.12 Where Do Distributions Come From? 26 1.13 The Binomial Process 28 1.14 Recommended Reading 29 2 Formulating Markov Chain Models 32 2.1 An Example 33 2.2 Modeling the Progress of Time 34 2.3 Modeling Possibilities as States 36 2.4 Simplifying Assumptions 38 2.5 Modeling Changes of State as Transitions 40 2.6 Obtaining the Data 45 2.7 Another Example 46 2.8 A Case Study 47 2.9 Higher Order Markov Chains 50 2.10 Reducing the Number of States 52 2.11 Nonstationary Markov Chains 53 2.12 Other Example 54 2.13 Summary 67 2.14 Recommended Reading 67 3 Markov Chain Calculations 72 3.1 Walk Probabilities 73 3.2 Transition Probabilities 74 3.3 State Probabilities 78 3.4 A Numerical Example 79 3.5 Expected Number of Visits 80 3.6 Sojourn Times 82 3.7 First Passage and Return Probabilities 83 3.8 Computational Formulas for All Markov Chains 86 3.9 Special Classes of Markov Chains 86 3.10 Steady-State Probabilities 87 3.11 The Uses of Steady-State Results 92 3.12 Mean First Passage Times 93 3.13 Computational Formulas for Ergodic Markov Chains 96 3.14 Terminating Markov Chains 96 3.15 Expected Number of Visits 98 3.16 Expected Duration of a Terminating Process 99 3.17 Absorption Probabilities 100 3.18 Hit Probabilities 102 3.19 Conditional Mean First Passage Times to Absorbing States 103 3.20 Computational Formulas for Terminating Processes 105 3.21 Call Center Calculations 105 3.22 Classification Terminology 106 3.23 Additional Complications in Infinite Chains 111 3.24 Dealing with a Reducible Process 112 3.25 Periodic Chains 113 3.26 Ergodic Chains 114 3.27 Recommended Reading 115 4 Rewards on Markov Chains 119 4.1 Formulation 120 4.2 A Numerical Example 120 4.3 Expected Total Reward 121 4.4 Random Variable Rewards 124 4.5 Semi-Markov Processes 126 4.6 Limiting Results for Ergodic Processes 126 4.7 Total Reward for Terminating Processes 130 4.8 Case Study 132 4.9 Discounting 133 4.10 Case Study 135 4.11 Recommended Reading 137 5 Continuous Time Markov Processes 140 5.1 An Example 141 5.2 Interpreting Transition Rates 146 5.3 The Assumptions Reconsidered 149 5.4 Aging Does Not Affect the Transition Time 150 5.5 Competing Transitions 152 5.6 Sojourn Times 153 5.7 Embedded Markov Chains 154 5.8 Deriving the Differential Equations 155 5.9 Solving the Differential Equations 157 5.10 State Probabilities 159 5.11 First Passage Probability Functions 159 5.12 State Classification 160 5.13 Steady-State Probabilities 161 5.14 Other Computable Quantities 163 5.15 Case Study 165 5.16 Birth-Death Processes 167 5.17 The Poisson Process 169 5.18 Properties of Poisson Processes 171 5.19 Khintchine’s Theorem 172 5.20 Phase-Type Distributions 173 5.21 Conclusions 175 5.22 Recommended Reading 175 6 Queueing Models 179 6.1 An Example 180 6.2 General Characteristics 182 6.3 Performance Measures 186 6.4 Relations Among Performance Measures 188 6.5 Little’s Formula 190 6.6 Markovian Queueing Models 191 6.7 The M/M/1 Model 193 6.8 The Significance of Traffic Intensity 198 6.9 Unnormalized Solutions 200 6.10 Limited Queue Capacity 202 6.11 Multiple Servers 204 6.12 Is It Better to Merge or Separate Servers? 207 6.13 Which is Better: More Servers or Faster Servers 208 6.14 Case Study: A Grain Elevator 209 6.15 The M/M/c/c and M/M/1 Models 210 6.16 Finite Sources 212 6.17 The Machine Repairmen Model 214 6.18 Numerical Calculations Using a Spreadsheet 214 6.19 Queue Discipline Variations 217 6.20 Non-Markovian Queues 218 6.21 The M/G/1 Model 219 6.22 Approximate Solutions for Other Models 220 6.23 Conclusion 221 6.24 Recommended Reading 221 7 Networks of Queues 225 7.1 Open Networks of Markovian Queues 226 7.2 An Example Open Network 227 7.3 Extensions 228 7.4 Closed Networks 229 7.5 A Preliminary Example 229 7.6 Relative Arrival Rates 230 7.7 Unnormalized Solutions for Individual Stations 232 7.8 Assembling the Pieces of the Solution 234 7.9 Calculating the Normalization Constant 235 7.10 Performance Measures for Closed Networks 237 7.11 Creating a Closed Model 239 7.12 Case Study 242 7.13 Extensions 247 7.14 Approximate Methods 247 7.15 Recommended Reading 248 8 Using the Transition Diagram to Compute 251 8.1 An Example 252 8.2 Definitions 254 8.3 Steady-State Probabilities 258 8.4 How to Generate All In-trees 259 8.5 Check Your Understanding 262 8.6 Generalization to Other Quantities 263 8.7 Mean First Passage Times 264 8.8 Results for Terminating Processes 265 8.9 How to Simplify the Arithmetic 266 8.10 How to Systematically Generate r-Forests 267 8.11 Summary of Results 267 8.12 How to Remember the Formulas 268 8.13 Advanced Topics 268 8.14 Recommended Reading 269 Appendix 1 271 Appendix 2 278 Index 300
£170.81
John Wiley & Sons Inc Stochastic Geometry and Its Applications
Book SynopsisAn extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences.Table of ContentsForeword to the first edition xiii From the preface to the first edition xvii Preface to the second edition xix Preface to the third edition xxi Notation xxiii 1 Mathematical foundations 1 1.1 Set theory 1 1.2 Topology in Euclidean spaces 3 1.3 Operations on subsets of Euclidean space 5 1.4 Mathematical morphology and image analysis 7 1.5 Euclidean isometries 9 1.6 Convex sets in Euclidean spaces 10 1.7 Functions describing convex sets 17 1.8 Polyconvex sets 24 1.9 Measure and integration theory 27 2 Point processes I: The Poisson point process 35 2.1 Introduction 35 2.2 The binomial point process 36 2.3 The homogeneous Poisson point process 41 2.4 The inhomogeneous and general Poisson point process 51 2.5 Simulation of Poisson point processes 53 2.6 Statistics for the homogeneous Poisson point process 55 3 Random closed sets I: The Boolean model 64 3.1 Introduction and basic properties 64 3.2 The Boolean model with convex grains 78 3.3 Coverage and connectivity 89 3.4 Statistics 95 3.5 Generalisations and variations 103 3.6 Hints for practical applications 106 4 Point processes II: General theory 108 4.1 Basic properties 108 4.2 Marked point processes 116 4.3 Moment measures and related quantities 120 4.4 Palm distributions 127 4.5 The second moment measure 139 4.6 Summary characteristics 143 4.7 Introduction to statistics for stationary spatial point processes 145 4.8 General point processes 156 5 Point processes III: Models 158 5.1 Operations on point processes 158 5.2 Doubly stochastic Poisson processes (Cox processes) 166 5.3 Neyman–Scott processes 171 5.4 Hard-core point processes 176 5.5 Gibbs point processes 178 5.6 Shot-noise fields 200 6 Random closed sets II: The general case 205 6.1 Basic properties 205 6.2 Random compact sets 213 6.3 Characteristics for stationary and isotropic random closed sets 216 6.4 Nonparametric statistics for stationary random closed sets 230 6.5 Germ–grain models 237 6.6 Other random closed set models 255 6.7 Stochastic reconstruction of random sets 276 7 Random measures 279 7.1 Fundamentals 279 7.2 Moment measures and related characteristics 284 7.3 Examples of random measures 286 8 Line, fibre and surface processes 297 8.1 Introduction 297 8.2 Flat processes 302 8.3 Planar fibre processes 314 8.4 Spatial fibre processes 330 8.5 Surface processes 333 8.6 Marked fibre and surface processes 339 9 Random tessellations, geometrical networks and graphs 343 9.1 Introduction and definitions 343 9.2 Mathematical models for random tessellations 346 9.3 General ideas and results for stationary planar tessellations 357 9.4 Mean-value formulae for stationary spatial tessellations 367 9.5 Poisson line and plane tessellations 370 9.6 STIT tessellations 375 9.7 Poisson-Voronoi and Delaunay tessellations 376 9.8 Laguerre tessellations 386 9.9 Johnson–Mehl tessellations 388 9.10 Statistics for stationary tessellations 390 9.11 Random geometrical networks 397 9.12 Random graphs 402 10 Stereology 411 10.1 Introduction 411 10.2 The fundamental mean-value formulae of stereology 413 10.3 Stereological mean-value formulae for germ–grain models 421 10.4 Stereological methods for spatial systems of balls 425 10.5 Stereological problems for nonspherical grains (shape-and-size problems) 436 10.6 Stereology for spatial tessellations 440 10.7 Second-order characteristics and directional distributions 444 References 453 Author index 507 Subject index 521
£76.90
John Wiley & Sons Inc Stochastic Claims Reserving Methods in Insurance
Book SynopsisCovers all the theory and practical advice that actuaries need in order to determine the claims reserves for non-life insurance. Describes all the necessary mathematical methods used to estimate loss reserves and shares the authors' practical experience, which is essential in showing which of the methods should be applied in any given situation.Table of ContentsPreface xi Acknowledgement xiii 1 Introduction and Notation 1 1.1 Claims process 1 1.1.1 Accounting principles and accident years 2 1.1.2 Inflation 3 1.2 Structural framework to the claims-reserving problem 5 1.2.1 Fundamental properties of the claims reserving process 7 1.2.2 Known and unknown claims 9 1.3 Outstanding loss liabilities, classical notation 10 1.4 General remarks 12 2 Basic Methods 15 2.1 Chain-ladder method (distribution-free) 15 2.2 Bornhuetter–Ferguson method 21 2.3 Number of IBNyR claims, Poisson model 25 2.4 Poisson derivation of the CL algorithm 27 3 Chain-Ladder Models 33 3.1 Mean square error of prediction 33 3.2 Chain-ladder method 36 3.2.1 Mack model (distribution-free CL model) 37 3.2.2 Conditional process variance 41 3.2.3 Estimation error for single accident years 44 3.2.4 Conditional MSEP, aggregated accident years 55 3.3 Bounds in the unconditional approach 58 3.3.1 Results and interpretation 58 3.3.2 Aggregation of accident years 63 3.3.3 Proof of Theorems 3.17, 3.18 and 3.20 64 3.4 Analysis of error terms in the CL method 70 3.4.1 Classical CL model 70 3.4.2 Enhanced CL model 71 3.4.3 Interpretation 72 3.4.4 CL estimator in the enhanced model 73 3.4.5 Conditional process and parameter prediction errors 74 3.4.6 CL factors and parameter estimation error 75 3.4.7 Parameter estimation 81 4 Bayesian Models 91 4.1 Benktander–Hovinen method and Cape–Cod model 91 4.1.1 Benktander–Hovinen method 92 4.1.2 Cape–Cod model 95 4.2 Credible claims reserving methods 98 4.2.1 Minimizing quadratic loss functions 98 4.2.2 Distributional examples to credible claims reserving 101 4.2.3 Log-normal/Log-normal model 105 4.3 Exact Bayesian models 113 4.3.1 Overdispersed Poisson model with gamma prior distribution 114 4.3.2 Exponential dispersion family with its associated conjugates 122 4.4 Markov chain Monte Carlo methods 131 4.5 Bühlmann–Straub credibility model 145 4.6 Multidimensional credibility models 154 4.6.1 Hachemeister regression model 155 4.6.2 Other credibility models 159 4.7 Kalman filter 160 5 Distributional Models 167 5.1 Log-normal model for cumulative claims 167 5.1.1 Known variances σj 2 170 5.1.2 Unknown variances 177 5.2 Incremental claims 182 5.2.1 (Overdispersed) Poisson model 182 5.2.2 Negative-Binomial model 183 5.2.3 Log-normal model for incremental claims 185 5.2.4 Gamma model 186 5.2.5 Tweedie’s compound Poisson model 188 5.2.6 Wright’s model 199 6 Generalized Linear Models 201 6.1 Maximum likelihood estimators 201 6.2 Generalized linear models framework 203 6.3 Exponential dispersion family 205 6.4 Parameter estimation in the EDF 208 6.4.1 MLE for the EDF 208 6.4.2 Fisher’s scoring method 210 6.4.3 Mean square error of prediction 214 6.5 Other GLM models 223 6.6 Bornhuetter–Ferguson method, revisited 223 6.6.1 MSEP in the BF method, single accident year 226 6.6.2 MSEP in the BF method, aggregated accident years 230 7 Bootstrap Methods 233 7.1 Introduction 233 7.1.1 Efron’s non-parametric bootstrap 234 7.1.2 Parametric bootstrap 236 7.2 Log-normal model for cumulative sizes 237 7.3 Generalized linear models 242 7.4 Chain-ladder method 244 7.4.1 Approach 1: Unconditional estimation error 246 7.4.2 Approach 3: Conditional estimation error 247 7.5 Mathematical thoughts about bootstrapping methods 248 7.6 Synchronous bootstrapping of seemingly unrelated regressions 253 8 Multivariate Reserving Methods 257 8.1 General multivariate framework 257 8.2 Multivariate chain-ladder method 259 8.2.1 Multivariate CL model 259 8.2.2 Conditional process variance 264 8.2.3 Conditional estimation error for single accident years 265 8.2.4 Conditional MSEP, aggregated accident years 272 8.2.5 Parameter estimation 274 8.3 Multivariate additive loss reserving method 288 8.3.1 Multivariate additive loss reserving model 288 8.3.2 Conditional process variance 295 8.3.3 Conditional estimation error for single accident years 295 8.3.4 Conditional MSEP, aggregated accident years 297 8.3.5 Parameter estimation 299 8.4 Combined Multivariate CL and ALR method 308 8.4.1 Combined CL and ALR method: the model 308 8.4.2 Conditional cross process variance 313 8.4.3 Conditional cross estimation error for single accident years 315 8.4.4 Conditional MSEP, aggregated accident years 319 8.4.5 Parameter estimation 321 9 Selected Topics I: Chain-Ladder Methods 331 9.1 Munich chain-ladder 331 9.1.1 The Munich chain-ladder model 333 9.1.2 Credibility approach to the MCL method 335 9.1.3 MCL Parameter estimation 340 9.2 CL Reserving: A Bayesian inference model 346 9.2.1 Prediction of the ultimate claim 351 9.2.2 Likelihood function and posterior distribution 351 9.2.3 Mean square error of prediction 354 9.2.4 Credibility chain-ladder 359 9.2.5 Examples 361 9.2.6 Markov chain Monte Carlo methods 364 10 Selected Topics II: Individual Claims Development Processes 369 10.1 Modelling claims development processes for individual claims 369 10.1.1 Modelling framework 370 10.1.2 Claims reserving categories 376 10.2 Separating IBNeR and IBNyR claims 379 11 Statistical Diagnostics 391 11.1 Testing age-to-age factors 391 11.1.1 Model choice 394 11.1.2 Age-to-age factors 396 11.1.3 Homogeneity in time and distributional assumptions 398 11.1.4 Correlations 399 11.1.5 Diagonal effects 401 11.2 Non-parametric smoothing 401 Appendix A: Distributions 405 A.1 Discrete distributions 405 A.1.1 Binomial distribution 405 A.1.2 Poisson distribution 405 A.1.3 Negative-Binomial distribution 405 A.2 Continuous distributions 406 A.2.1 Uniform distribution 406 A.2.2 Normal distribution 406 A.2.3 Log-normal distribution 407 A.2.4 Gamma distribution 407 A.2.5 Beta distribution 408 Bibliography 409 Index 417
£78.38
John Wiley & Sons Inc Probability Statistics and Stochastic Processes
Book SynopsisPraise for the First Edition . . . an excellent textbook . . . well organized and neatly written. Mathematical Reviews . . . amazingly interesting . . . Technometrics Thoroughly updated to showcase the interrelationships between probability, statistics, and stochastic processes, Probability, Statistics, and Stochastic Processes, Second Edition prepares readers to collect, analyze, and characterize data in their chosen fields. Beginning with three chapters that develop probability theory and introduce the axioms of probability, random variables, and joint distributions, the book goes on to present limit theorems and simulation. The authors combine a rigorous, calculus-based development of theory with an intuitive approach that appeals to readers'' sense of reason and logic. Including more than 400 examples that help illustrate concepts and theory, the Second Edition features new material on statiTable of ContentsPreface xi Preface to the First Edition xiii 1 Basic Probability Theory 1 1.1 Introduction 1 1.2 Sample Spaces and Events 3 1.3 The Axioms of Probability 7 1.4 Finite Sample Spaces and Combinatorics 15 1.4.1 Combinatorics 17 1.5 Conditional Probability and Independence 27 1.6 The Law of Total Probability and Bayes’ Formula 41 Problems 63 2 Random Variables 76 2.1 Introduction 76 2.2 Discrete Random Variables 77 2.3 Continuous Random Variables 82 2.4 Expected Value and Variance 95 2.5 Special Discrete Distributions 111 2.6 The Exponential Distribution 123 2.7 The Normal Distribution 127 2.8 Other Distributions 131 2.9 Location Parameters 137 2.10 The Failure Rate Function 139 Problems 144 3 Joint Distributions 156 3.1 Introduction 156 3.2 The Joint Distribution Function 156 3.3 Discrete Random Vectors 158 3.4 Jointly Continuous Random Vectors 160 3.5 Conditional Distributions and Independence 164 3.5.1 Independent Random Variables 168 3.6 Functions of Random Vectors 172 3.7 Conditional Expectation 185 3.8 Covariance and Correlation 196 3.9 The Bivariate Normal Distribution 209 3.10 Multidimensional Random Vectors 216 3.11 Generating Functions 231 3.12 The Poisson Process 240 Problems 247 4 Limit Theorems 263 4.1 Introduction 263 4.2 The Law of Large Numbers 264 4.3 The Central Limit Theorem 268 4.4 Convergence in Distribution 275 Problems 278 5 Simulation 281 5.1 Introduction 281 5.2 Random Number Generation 282 5.3 Simulation of Discrete Distributions 283 5.4 Simulation of Continuous Distributions 285 5.5 Miscellaneous 290 Problems 292 6 Statistical Inference 294 6.1 Introduction 294 6.2 Point Estimators 294 6.3 Confidence Intervals 304 6.4 Estimation Methods 312 6.5 Hypothesis Testing 327 6.6 Further Topics in Hypothesis Testing 334 6.7 Goodness of Fit 339 6.8 Bayesian Statistics 351 6.9 Nonparametric Methods 363 Problems 378 7 Linear Models 391 7.1 Introduction 391 7.2 Sampling Distributions 392 7.3 Single Sample Inference 395 7.4 Comparing Two Samples 402 7.5 Analysis of Variance 409 7.6 Linear Regression 415 7.7 The General Linear Model 431 Problems 436 8 Stochastic Processes 444 8.1 Introduction 444 8.2 Discrete -Time Markov Chains 445 8.3 Random Walks and Branching Processes 464 8.4 Continuous -Time Markov Chains 475 8.5 Martingales 494 8.6 Renewal Processes 502 8.7 Brownian Motion 509 Problems 517 Appendix A Tables 527 Appendix B Answers to Selected Problems 535 Further Reading 551 Index 553
£102.56
John Wiley & Sons Inc Operational Subjective Statistical Methods
Book SynopsisMethods of subjective statistical analysis have seen a resurgence of activity in the last decade. This book treats the theory of probability and the logic of uncertainty in a systematic way. It features a technical presentation of the mathematical impact of personal beliefs and values on statistical analysis.Trade Review"...has a merit for everyone who wonders about the foundations ofinference..." (Australian & New Zealand J Statistics, 2000)Table of ContentsPhilosophical and Historical Introduction. Quantities, Prevision, and Coherency. Coherent Statistical Inference. Related Forms for Asserting Uncertain Knowledge. Distribution Functions. Proper Scoring Rules. The Multivariate Normal Distribution and Its Mixtures. Sequential Forecasting Based on Linear Conditional PrevisionStructures: Theory and Practice of Linear Regression. The Direction of Statistical Research. References. Index.
£157.45
John Wiley & Sons Inc Statistical Methods in Analytical Chemistry
Book SynopsisThis edition continues to provide analytical chemists and statisticians with the latest practical information on using statistical tools in chemical data analysis. The accompanying FTP site contains a series of programs that illustrate the statistical techniques which are discussed in the book.Trade Review“This new edition of a successful, bestselling book continues to provide you with practical information on the useof statistical methods for solving real-world problems in complex industrial environments.” (PDFCHM Online, 27 February 2013) "...a comprehensive, very useful and clear guide for all analytical chemists..." (Annali di Chimica, Vol 153, 2000) "Substantially updated...for lab supervisors and project mangers, and is useful...for advanced students of chemistry and pharmaceutical science." (SciTech Book News, Vol. 24, No. 2, June 2001) "Its clarity, focus and logical approach to statistical analysis of chemical data make it a book that should appear on the bookshelf of most analytical chemists." (Journal of the American Chemical Society, Vol. 123 No. 36)Table of ContentsUnivariate Data. Bi- and Multivariate Data. Related Topics. Complex Examples. Appendices. Technical Tidbits. Glossary. References. Index.
£175.46
John Wiley & Sons Inc Numerical Methods for Stochastic Processes
Book SynopsisThis study deals with the calculations of mathematical expectations, primarily by simulation methods. The authors explore the present state of research and signal the types of problems raised by new methods. Topics discussed include Monte Carlo methods and the simulation of stochastic processes.Table of ContentsPreliminaries. Computation of Expectations in Finite Dimension. Simulation of Random Processes. Deterministic Resolution of Some Markovian Problems. Stochastic Differential Equations and Brownian Functionals. Notes. References. Index.
£184.46
John Wiley & Sons Inc Counting Processes and Survival Analysis
Book SynopsisThis book explores the martingale approach to the statistical analysis of counting processes, with an emphasis on application of those methods to censored failure time data. Introduced in the 1970s, this approach has proven to be remarkably successful in yielding results about statistical methods for many problems arising in censored data.Trade Review"…a unique source for combining the theory and the application of the survival analysis with censored data." (Technometrics, August 2007)Table of ContentsPreface. 0. The Applied Setting. 1. The Counting Process and Martingale Framework. 2. Local Square Integrable Martingales. 3. Finite Sample Moments and Large Sample Consistency of Tests and Estimators. 4. Censored Data Regression Models and Their Application. 5. Martingale Central Limit Theorem. 6. Large Sample results of the Kaplan-Meier Estimator. 7. Weighted Logrank Statistics. 8. Distribution Theory for Proportional Hazards Regression. Appendix A: Some Results from stieltjes Integration and Probability Theory. Appendix B: An Introduction to Weak convergence. Appendix C: The Martingale Central Limit Theorem: Some Preliminaries. Appendix D: Data. Appendix E: Exercises. Bibliography. Notation. Author Index. Subject Index.
£101.66
John Wiley & Sons Inc Practical Statistics for Experimental Biologists
Book SynopsisA good working knowledge of statistical principles is needed for both the design and analysis of biological experiments and the subsequent handling of the large amounts of data generated if worthwhile, reliable conclusions are to be reached. Practical Statistics for Experimental Biologists, Second Edition provides biologists with a user-friendly, non-technical introduction to the basics of statistics. The book has been thoroughly revised and updated to incorporate: * Worked examples and printouts from MINITAB * Relevant case studies and applications * Further Notes section for background explanations Written by a biologist with extensive experience of applying statistical procedures to experimental systems, this book will be invaluable to undergraduates, postgraduates and researchers in microbiology, immunology, biochemistry, botany, zoology, physiology, pharmacology and pharmacy. Review of the First Edition ...strongly recommended as the current first choicTrade Review"...a refreshing and useful book..." ---- Trends in Plant Science, September 2000Table of ContentsA Simple Experiment in Pipetting. How to Condense the Bulkiness of Data. Are Those Differences Significant? More About Measurement Differences. Awkward-Measurement Data. How to Deal with Count Data. How to Deal with Proportion Data. Correlation and Regression. Dose-Response Lines and Assays. References. Additional Reading. Appendices. Index.
£62.96
Harvard University Press Randomness
Book SynopsisThis book is aimed at the trouble with trying to learn about probability. A story of the misconceptions and difficulties civilization overcame in progressing toward probabilistic thinking, Randomness is also a skillful account of what makes the science of probability so daunting in our own day.Trade ReviewClearly, the computation of probabilities is not just an arid game… As Deborah Bennett shows in her excellent little book on the mathematics of chance, the concept has been controversial for thousands of years… [Her] cultured and accessible book goes a long way towards demystifying the science of probability and thereby offers the reader a useful variety of conceptual tools with which to probe the future and illuminate the present. -- Steven Poole * The Guardian *[Randomness] can most easily be described as a brief history of chance… I can cheerfully recommend it to anyone who is a total beginner when it comes to probability, what it means, why it is desperately puzzling, and what it can do for us despite that… It is fascinating to read about the pioneers of probability, such as Pierre Simon de Laplace with his ‘normal distribution’—now more familiar as the notorious bell curve—and Adolphe Quetelet, perhaps the first to realise that there are statistical patterns in human behaviour. And I applaud the blunt reminder that when it comes to the real world the ‘normal’ distribution is actually highly abnormal… My main criticism: it left me wanting more. A sequel, please. -- Ian Stewart * Times Higher Education Supplement *Chances are high that reading this book will clear up your misconceptions about randomness and probabilities. In this very entertaining little book, simply written but intended for careful readers, some of the most common mistakes people make about chance are carefully analyzed. While describing interesting aspects of the mathematics of probability, the author takes frequent detours into the history of humanity’s understanding (and misunderstanding) of the laws of chance, touching on subjects as diverse as chance in decision-making and the fairness of those decisions, gambling and our intuitive understanding of chance, the likelihood of the extremely rare, the existence of true randomness and how computers have helped shape modern thinking about probabilities… An insightful chapter is ‘Chance or Necessity?’ The question is very, very old (determinism versus chaos), and the answer is not clear even today. The author describes the problem beautifully: ‘Is random outcome completely determined, and random only by virtue of our ignorance of the most minute contributing factors?’ Einstein grappled with this conundrum until his death and never ceased to combat the idea that God could conceivably throw dice… Whether well-educated in mathematics or not, people have always been fascinated by randomness and intrigued by the fundamental question of the real nature of randomness, of how you can tell randomness from something that is not. -- J. A. Rial * American Scientist *The great strength of this book is the way it uses history and even prehistory of probability to chart its present territory and cast light on its core point of contention: does true randomness exist in nature, or is it only a psychological artefact?… Bennett’s text…is like a café conversation between likable cognoscenti…nothing could more provoke and excite the reader. -- Simon Ings * New Scientist *In this book, Bennett seeks to account for the centuries-long lapse between early uses of chance in decision making and the more technical studies of probability first undertaken in the seventeenth century. At the same time, she explores the confusions and misunderstandings about probability that persist today. She argues that the notion of randomness played a crucial role in inhibiting conceptual progress in probability and that it also accounts for present-day struggles to come to terms with the subject… Bennett’s book is written in a lucid, engaging style and provides an entertaining introduction to some questions in probability. -- Patti Wilger Hunter * Isis *[A] sharp analysis of the way we assess probability in everyday life. -- Robert Winder * New Statesman & Society *Randomness, by mathematician Deborah J. Bennett, was obviously a labor of love. The result is an interesting book that combines a well-researched, anecdotally presented survey of the history of chance, probability and randomness along with some elementary instruction in probability… It includes a wide-ranging and rich bibliography that reflects the passion of the author for the subject. Anybody interested in gaming, random numbers, the Monte Carlo method and so on will find nice anecdotal descriptions of these topics, together with detailed notes and references to the bibliography for more detailed study. It is a good book to have. -- Stephen Gasiorowicz * Physics Today *In 1996 Charles Hailey and David Helfand reported their calculations of the odds of a commercial airliner being struck by a meteor, in response to speculation about TWA flight 800… They conclude that, in over 30 years of air travel, the probability that a commercial flight would have been hit by a meteor big enough to crash it is 1 in 10. This bit of probability trivia is an indication of human beings continuous struggle to understand probability and chance through the ages, and Deborah Bennett captures the fascination with numbers in this pocket-sized volume. The book is filled with…gems. * Skeptic *This volume is exceptionally readable. It takes away much of the mystery of probability while adding to our sense of wonder. * Wordtrade *The fact that randomness, agency, and holiness can readily displace each other in phenomenological explanations of human action is the central concern that might draw students of consciousness to Bennett’s book. Bennett does an excellent job, explaining and drawing out the major questions that swirl around the randomness–agency–holiness issue. -- T. W. Draper * Journal of Consciousness Studies *[This book] examines randomness and several other notions that were critical to the historical development of probabilistic thinking and that also play an important role in any individual’s understanding of the laws of chance. [It] addresses why, from ancient times to today, people have resorted to chance in making decisions; whether a decision made by random choice is a fair decision; how to figure the odds; what role gambling has played in understanding chance; whether extremely rare events are likely in the long run; why some societies and individuals reject randomness; whether true randomness exists; the view of randomness as uncertainty; why even experts disagree about the many meanings of randomness; and why probability is so counterintuitive. * Journal of Economic Literature *Mathematics is its own language, and sometimes it doesn’t translate readily into other human tongues. But Bennett is brilliantly bilingual, well able to put mathematical concepts into clear, expressive English. Her topic is intrinsically fascinating, for who has not felt buffeted by random events, and who has not sought to see when the wheel of fortune may turn up good luck?… More than an intriguing exploration of a peculiarly fascinating part of mathematics, its coverage, ranging from ancient games of chance to modern probability mind-games, makes it comprehensive as well as compulsively readable. -- Patricia Monaghan * Booklist *A clear and detailed examination of the role of pure chance, with fascinating historical asides. * Kirkus Reviews *A careful and well-written treatment of an intriguing subject. -- Donald Goldsmith, author of The Ultimate EinsteinRandomness tells us about chance by recalling the real history of probability and solving many of its engaging puzzles. Beginners will find themselves welcomed and well led. -- Frederick Mosteller, Harvard UniversityRandomness explains probability and odds in an accessible way. This book puts risk and chance into perspective for the airline passenger and the lottery player alike. -- Henry Petroski, author of Invention by Design: How Engineers Get from Thought to ThingTable of Contents* Chance Encounters * Why Resort to Chance? * When the Gods Played Dice * Figuring the Odds * Thought Games for Gamblers * Chance or Necessity? * Order in Apparent Chaos * Wanted: Random Numbers * Randomness as Uncertainty * Paradoxes in Probability * Notes * Bibliography * Index
£24.26
Princeton University Press Quantal Response Equilibrium A Stochastic Theory
Book SynopsisQuantal Response Equilibrium presents a stochastic theory of games that unites probabilistic choice models developed in psychology and statistics with the Nash equilibrium approach of classical game theory. Nash equilibrium assumes precise and perfect decision making in games, but human behavior is inherently stochastic and people realize that theTrade Review"This book brings together two decades of scholarship on an important model of boundedly rational behavior in strategic decision-making settings. Including numerous important applications in economics, political science, and pure game theory, this unified treatment will be valuable to a wide range of scholars."—Timothy Cason, Purdue University"Quantal response equilibrium is a standard tool for game theorists and has numerous connections to other tools and applications. This book collects and extends existing material on QRE and is a significant contribution to pure, and especially applied, game theory. No other books explicate QRE systematically beyond the introductory level and these authors are the right team for pulling the core material together."—Daniel Friedman, University of California, Santa Cruz"Well-written and easy to follow, this book covers the topic of quantal response equilibrium. The notion of stochastic equilibrium has changed the way game theorists think about long-run and short-run equilibrium. Written by three leading experts, this book is of great importance to researchers in economic theory and political science, and to graduate students."—David K. Levine, European University InstituteTable of Contents*Frontmatter, pg. i*Contents, pg. v*Preface, pg. ix*1. Introduction and Background, pg. 1*2. Quantal Response Equilibrium in Normal-Form Games, pg. 10*3. Quantal Response Equilibrium in Extensive-Form Games, pg. 63*4. Heterogeneity, pg. 88*5. Dynamics and Learning, pg. 112*6. QRE as a Structural Model for Estimation, pg. 141*7. Applications to Game Theory, pg. 161*8. Applications to Political Science, pg. 206*9. Applications to Economics, pg. 248*10. Epilogue: Some Thoughts about Future Research, pg. 281*References, pg. 291*Index, pg. 301
£52.20
Princeton University Press Diffusion Quantum Theory and Radically Elementary
Book SynopsisExplains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. This book shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis.Table of Contents*FrontMatter, pg. i*Contents, pg. vii*Preface, pg. ix*Chapter One. Introduction: Diffusive Motion and Where It Leads, pg. 1*Chapter Two. Hypercontractivity, Logarithmic Sobolev Inequalities, and Applications: A Survey of Surveys, pg. 45*Chapter Three. Ed Nelson's Work in Quantum Theory, pg. 75*Chapter Four Symanzik, Nelson, and Self-Avoiding Walk, pg. 95*Chapter Five. Stochastic Mechanics: A Look Back and a Look Ahead, pg. 117*Chapter Six. Current Trends in Optimal Transportation: A Tribute to Ed Nelson, pg. 141*Chapter Seven. Internal Set Theory and Infinitesimal Random Walks, pg. 157*Chapter Eight. Nelson's Work on Logic and Foundations and Other Reflections on the Foundations of Mathematics, pg. 183*Chapter Nine. Some Musical Groups: Selected Applications of Group Theory in Music, pg. 209*Chapter Ten. Afterword, pg. 229*Appendix A. Publications by Edward Nelson, pg. 233*Index, pg. 241
£63.75
Princeton University Press Nonlinear Dynamical Systems and Control
Book SynopsisPresents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods. This graduate-level textbook is suitable for applied mathematicians, dynamical systems theorists, control theorists, and engineers.Trade ReviewWassim Haddad, Winner of the 2014 Pendray Aerospace Literature Award, American Institute of Aeronautics and Astronautics "The book is lucid and well written and contains numerous worked examples for specific applications to important classes of systems as well as numerous problems and suggestions for further study at the end of the main chapters. This book will be an excellent source of reference materials for graduate students of applied mathematics, control theorists and engineers studying the stability theory of dynamical systems and controls. It will also be a rich source of materials for self study by researchers and practitioners interested in systems theory of engineering, controls, computer science, chemistry, life sciences and economics."--Olusola Akinyele, Mathematical ReviewsTable of ContentsConventions and Notation xv Preface xxi Chapter 1. Introduction 1 Chapter 2. Dynamical Systems and Differential Equations 9 Chapter 3. Stability Theory for Nonlinear Dynamical Systems 135 Chapter 4. Advanced Stability Theory 207 Chapter 5. Dissipativity Theory for Nonlinear Dynamical Systems 325 Chapter 6. Stability and Optimality of Feedback Dynamical Systems 411 Chapter 7. Input-Output Stability and Dissipativity 471 Chapter 8. Optimal Nonlinear Feedback Control 511 Chapter 9. Inverse Optimal Control and Integrator Backstepping 557 Chapter 10. Disturbance Rejection Control for Nonlinear Dynamical Systems 603 Chapter 11. Robust Control for Nonlinear Uncertain Systems 649 Chapter 12. Structured Parametric Uncertainty and Parameter-Dependent Lyapunov Functions 719 Chapter 13. Stability and Dissipativity Theory for Discrete-Time Nonlinear Dynamical Systems 763 Chapter 14. Discrete-Time Optimal Nonlinear Feedback Control 845 Bibliography 901 Index 939
£120.70
Princeton University Press Mathematical Analysis of Deterministic and
Book SynopsisElectromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. This book introduces the electromagnetics of complex media through a systematic account of their mathematical theory.Trade Review"This monograph is of a very high standard, allowing the reader to learn many facets of the rapidly growing field of complex media and to get up-to-date information on a number of open research problems."--Vilmos Komornik, Mathematical ReviewsTable of ContentsPreface xi PART 1. MODELLING AND MATHEMATICAL PRELIMINARIES 1 Chapter 1. Complex Media 3 Chapter 2. The Maxwell Equations and Constitutive Relations 9 2.1 Introduction 9 2.2 Fundamentals 9 2.3 Constitutive relations 13 2.4 The Maxwell equations in complex media: A variety of problems 23 Chapter 3. Spaces and Operators 38 3.1 Introduction 38 3.2 Function spaces 38 3.3 Standard difierential and trace operators 45 3.4 Function spaces for electromagnetics 48 3.5 Traces 51 3.6 Various decompositions 52 3.7 Compact embeddings 53 3.8 The operators of vector analysis revisited 54 3.9 The Maxwell operator 56 PART 2. TIME-HARMONIC DETERMINISTIC PROBLEMS 59 Chapter 4. Well Posedness 61 4.1 Introduction 61 4.2 Solvability of the interior problem 62 4.3 The eigenvalue problem 68 4.4 Low chirality behaviour 70 4.5 Comments on exterior domain problems 74 4.6 Towards numerics 77 Chapter 5. Scattering Problems: Beltrami Fields and Solvability 83 5.1 Introduction 83 5.2 Elliptic, circular and linear polarisation of waves 84 5.3 Beltrami fields - The Bohren decomposition 86 5.4 Scattering problems: Formulation 88 5.5 An introduction to BIEs 91 5.6 Properties of Beltrami fields 96 5.7 Solvability 99 5.8 Generalised Muller's BIEs 106 5.9 Low chirality approximations 108 5.10 Miscellanea 109 Chapter 6. Scattering Problems: A Variety of Topics 112 6.1 Introduction 112 6.2 Important concepts of scattering theory 113 6.3 Back to chiral media: Scattering relations and the far-field operator 118 6.4 Using dyadics 124 6.5 Herglotz wave functions 129 6.6 Domain derivative 136 6.7 Miscellanea 140 PART 3. TIME-DEPENDENT DETERMINISTIC PROBLEMS 149 Chapter 7. Well Posedness 151 7.1 Introduction 151 7.2 The Maxwell equations in the time domain 151 7.3 Functional framework and assumptions 152 7.4 Solvability 153 7.5 Other possible approaches to solvability 158 7.6 Miscellanea 162 Chapter 8. Controllability 163 8.1 Introduction 163 8.2 Formulation 163 8.3 Controllability of achiral media: The Hilbert Uniqueness method 165 8.4 The forward and backward problems 167 8.5 Controllability: Complex media 174 8.6 Miscellanea 176 Chapter 9. Homogenisation 180 9.1 Introduction 180 9.2 Formulation 181 9.3 A formal two-scale expansion 184 9.4 The optical response region 188 9.5 General bianisotropic media 199 9.6 Miscellanea 207 Chapter 10. Towards a Scattering Theory 212 10.1 Introduction 212 10.2 Formulation 213 10.3 Some basic strategies 214 10.4 On the construction of solutions 217 10.5 Wave operators and their construction 220 10.6 Complex media electromagnetics 225 10.7 Miscellanea 229 Chapter 11. Nonlinear Problems 231 11.1 Introduction 231 11.2 Formulation 231 11.3 Well posedness of the model 232 11.4 Miscellanea 241 PART 4. STOCHASTIC PROBLEMS 245 Chapter 12. Well Posedness 247 12.1 Introduction 247 12.2 Maxwell equations for random media 248 12.3 Functional setting 249 12.4 Well posedness 250 12.5 Other possible approaches to solvability 255 12.6 Miscellanea 261 Chapter 13. Controllability 263 13.1 Introduction 263 13.2 Formulation 263 13.3 Subtleties of stochastic controllability 264 13.4 Approximate controllability I: Random PDEs 266 13.5 Approximate controllability II: BSPDEs 269 13.6 Miscellanea 272 Chapter 14. Homogenisation 275 14.1 Introduction 275 14.2 Ergodic media 276 14.3 Formulation 279 14.4 A formal two-scale expansion 282 14.5 Homogenisation of the Maxwell system 284 14.6 Miscellanea 288 PART 5. APPENDICES 291 Appendix A. Some Facts from Functional Analysis 293 A.1 Duality 293 A.2 Strong, weak and weak-* convergence 295 A.3 Calculus in Banach spaces 297 A.4 Basic elements of spectral theory 300 A.5 Compactness criteria 303 A.6 Compact operators 304 A.7 The Banach-Steinhaus theorem 308 A.8 Semigroups and the Cauchy problem 308 A.9 Some fixed point theorems 312 A.10 The Lax-Milgram lemma 313 A.11 Gronwall's inequality 314 A.12 Nonlinear operators 315 Appendix B. Some Facts from Stochastic Analysis 316 B.1 Probability in Hilbert spaces 316 B.2 Stochastic processes and random fields 318 B.3 Gaussian measures 319 B.4 The Q- and the cylindrical Wiener process 320 B.5 The Ito integral 321 B.6 Ito formula 324 B.7 Stochastic convolution 325 B.8 SDEs in Hilbert spaces 325 B.9 Martingale representation theorem 326 Appendix C. Some Facts from Elliptic Homogenisation Theory 327 C.1 Spaces of periodic functions 327 C.2 Compensated compactness 329 C.3 Homogenisation of elliptic equations 329 C.4 Random elliptic homogenisation theory 332 Appendix D. Some Facts from Dyadic Analysis (by George Dassios) 334 Appendix E. Notation and abbreviations 341 Bibliography 343 Index 377
£106.20
Princeton University Press Degenerate Diffusion Operators Arising in
Book SynopsisThis book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the Martingale problem aTable of ContentsPreface xi 1 Introduction 1*1.1 Generalized Kimura Diffusions 3 *1.2 Model Problems 5 *1.3 Perturbation Theory 9 *1.4 Main Results 10 *1.5 Applications in Probability Theory 13 *1.6 Alternate Approaches 14 *1.7 Outline of Text 16 *1.8 Notational Conventions 20 I Wright-Fisher Geometry and the Maximum Principle 23 2 Wright-Fisher Geometry 25*2.1 Polyhedra and Manifolds with Corners 25 *2.2 Normal Forms and Wright-Fisher Geometry 29 3 Maximum Principles and Uniqueness Theorems 34*3.1 Model Problems 34 *3.2 Kimura Diffusion Operators on Manifolds with Corners 35 *3.3 Maximum Principles for theHeat Equation 45 II Analysis of Model Problems 49 4 The Model Solution Operators 51*4.1 The Model Problemin 1-dimension 51 *4.2 The Model Problem in Higher Dimensions 54 *4.3 Holomorphic Extension 59 *4.4 First Steps Toward Perturbation Theory 62 5 Degenerate Holder Spaces 64*5.1 Standard Holder Spaces 65 *5.2 WF-Holder Spaces in 1-dimension 66 6 Holder Estimates for the 1-dimensional Model Problems 78*6.1 Kernel Estimates for Degenerate Model Problems 80 *6.2 Holder Estimates for the 1-dimensional Model Problems 89 *6.3 Propertiesof the Resolvent Operator 103 7 Holder Estimates for Higher Dimensional CornerModels 107*7.1 The Cauchy Problem 109 *7.2 The Inhomogeneous Case 122 *7.3 The Resolvent Operator 135 8 Holder Estimates for Euclidean Models 137*8.1 Holder Estimates for Solutions in the Euclidean Case 137 *8.2 1-dimensional Kernel Estimates 139 9 Holder Estimates for General Models 143*9.1 The Cauchy Problem 145 *9.2 The Inhomogeneous Problem 149 *9.3 Off-diagonal and Long-time Behavior 166 *9.4 The Resolvent Operator 169 III Analysis of Generalized Kimura Diffusions 179 10 Existence of Solutions 181*10.1 WF-Holder Spaces on a Manifold with Corners 182 *10.2 Overview of the Proof 187 *10.3 The Induction Argument 191 *10.4 The Boundary Parametrix Construction 194 *10.5 Solution of the Homogeneous Problem 205 *10.6 Proof of the Doubling Theorem 208 *10.7 The Resolvent Operator and C0-Semi-group 209 *10.8 Higher Order Regularity 211 11 The Resolvent Operator 218*11.1 Construction of the Resolvent 220 *11.2 Holomorphic Semi-groups 229 *11.3 DiffusionsWhere All Coefficients Have the Same Leading Homogeneity 230 12 The Semi-group on C0(P) 235*12.1 The Domain of the Adjoint 237 *12.2 The Null-space of L 240 *12.3 Long Time Asymptotics 243 *12.4 Irregular Solutions of the Inhomogeneous Equation 247 A Proofs of Estimates for the Degenerate 1-d Model 251* A.1 Basic Kernel Estimates 252 * A.2 First Derivative Estimates 272 * A.3 Second Derivative Estimates 278 * A.4 Off-diagonal and Large-t Behavior 291 Bibliography 301 Index 305
£72.00
MP-AMM American Mathematical Stochastic Integrals
Book SynopsisPresents Brownian motion and deals with stochastic integrals and differentials, including Ito lemma. This book is devoted to topics of stochastic integral equations and stochastic integral equations on smooth manifolds. It is suitable for graduate students and researchers interested in probability, stochastic processes, and their applications.Table of ContentsBrownian motion Stochastic integrals and differentials Stochastic integral equations $(d=1)$ Stochastic integral equations $(d\geq2)$ References Subject index Errata.
£54.90
Society for Industrial and Applied Mathematics Foundations of Stochastic Differential Equations
Book SynopsisA systematic, self-contained treatment of the theory of stochastic differential equations in infinite dimensional spaces. Included is a discussion of Schwartz spaces of distributions in relation to probability theory and infinite dimensional stochastic analysis, as well as the random variables and stochastic processes that take values in infinite dimensional spaces.
£44.96
John Wiley & Sons Inc Stochastic Structural Dynamics Application of
Book SynopsisOne of the first books to provide in-depth and systematic application of finite element methods to the field, Stochastic Structural Dynamics presents and illustrates direct integration methods for analyzing the statistics of the response of structures to stochastic loads.Table of ContentsDedication xi Preface xiii Acknowledgements xv 1. Introduction 1 1.1 Displacement Formulation Based Finite Element Method 2 1.2 Element Equations of Motion for Temporally and Spatially Stochastic Systems 13 1.3 Hybrid Stress Based Element Equations of Motion 14 1.4 Incremental Variational Principle and Mixed Formulation Based Nonlinear Element Matrices 18 1.5 Constitutive Relations and Updating of Configurations and Stresses 36 1.6 Concluding Remarks 48 References 49 2. Spectral Analysis and Response Statistics of Linear Structural Systems 53 2.1 Spectral Analysis 53 2.2 Evolutionary Spectral Analysis 56 2.3 Evolutionary Spectra of Engineering Structures 60 2.4 Modal Analysis and Time-Dependent Response Statistics 76 2.5 Response Statistics of Engineering Structures 79 References 94 3. Direct Integration Methods for Linear Structural Systems 97 3.1 Stochastic Central Difference Method 97 3.2 Stochastic Central Difference Method with Time Co-ordinate Transformation 100 3.3 Applications 102 3.4 Extended Stochastic Central Difference Method and Narrow-band Force Vector 114 3.5 Stochastic Newmark Family of Algorithms 122 References 128 4. Modal Analysis and Response Statistics of Quasi-linear Structural Systems 131 4.1 Modal Analysis of Temporally Stochastic Quasi-linear Systems 131 4.2 Response Analysis Based on Melosh-Zienkiewicz-Cheung Bending Plate Finite Element 141 4.3 Response Analysis Based on High Precision Triangular Plate Finite Element 156 4.4 Concluding Remarks 166 References 166 5. Direct Integration Methods for Response Statistics of Quasi-linear Structural Systems 169 5.1 Stochastic Central Difference Method for Quasi-linear Structural Systems 169 5.2 Recursive Covariance Matrix of Displacements of Cantilever Pipe Containing Turbulent Fluid 174 5.3 Quasi-linear Systems under Narrow-band Random Excitations 184 5.4 Concluding Remarks 188 References 190 6. Direct Integration Methods for Temporally Stochastic Nonlinear Structural Systems 191 6.1 Statistical Linearization Techniques 191 6.2 Symplectic Algorithms of Newmark Family of Integration Schemes 194 6.3 Stochastic Central Difference Method with Time Co-ordinate Transformation and Adaptive Time Schemes 199 6.4 Outline of steps in computer program 211 6.5 Large Deformations of Plate and Shell Structures 213 6.6 Concluding Remarks 224 References 226 7. Direct Integration Methods for Temporally and Spatially Stochastic Nonlinear Structural Systems 231 7.1 Perturbation Approximation Techniques and Stochastic Finite Element Methods 232 7.2 Stochastic Central Difference Methods for Temporally and Spatially Stochastic Nonlinear Systems 241 7.3 Finite Deformations of Spherical Shells with Large Spatially Stochastic Parameters 251 7.4 Closing Remarks 255 References 257 Appendices 1A Mass and Stiffness Matrices of Higher Order Tapered Beam Element 261 1B Consistent Stiffness Matrix of Lower Order Triangular Shell Element 267 1B.1 Inverse of Element Generalized Stiffness Matrix 267 1B.2 Element Leverage Matrices 268 1B.3 Element Component Stiffness Matrix Associated with Torsion 271 References 276 1C Consistent Mass Matrix of Lower Order Triangular Shell Element 277 Reference 280 2A Eigenvalue Solution 281 References 282 2B Derivation of Evolutionary Spectral Densities and Variances of Displacements 283 2B.1 Evolutionary Spectral Densities Due to Exponentially Decaying Random Excitations 283 2B.2 Evolutionary Spectral Densities Due to Uniformly Modulated Random Excitations 286 2B.3 Variances of Displacements 288 References 297 2C Time-dependent Covariances of Displacements 299 2D Covariances of Displacements and Velocities 311 2E Time-dependent Covariances of Velocities 317 2F Cylindrical Shell Element Matrices 323 3A Deterministic Newmark Family of Algorithms 327 Reference 331 Index 333
£91.76
John Wiley & Sons Inc Stochastic Differential Equations
Book SynopsisA beginner's guide to stochastic growth modeling The chief advantage of stochastic growth models over deterministic models is that they combine both deterministic and stochastic elements of dynamic behaviors, such as weather, natural disasters, market fluctuations, and epidemics. This makes stochastic modeling a powerful tool in the hands of practitioners in fields for which population growth is a critical determinant of outcomes. However, the background requirements for studying SDEs can be daunting for those who lack the rigorous course of study received by math majors. Designed to be accessible to readers who have had only a few courses in calculus and statistics, this book offers a comprehensive review of the mathematical essentials needed to understand and apply stochastic growth models. In addition, the book describes deterministic and stochastic applications of population growth models including logistic, generalized logistic, Gompertz, negative exponentiTrade Review"An indispensable resource for students and practitioners with limited exposure tomathematics and statistics, Stochastic Differential Equations: An Introduction withApplications in Population Dynamics Modeling is an excellent fit for advanced under-graduates and beginning graduate students, as well as practitioners who need a gentleintroduction to SDEs" Mathematical Reviews, October 2017Table of ContentsDedication x Preface xi Symbols and Abbreviations xiii 1 Mathematical Foundations 1: Point-Set Concepts, Set and Measure Functions, Normed Linear Spaces, and Integration 1 1.1 Set Notation and Operations 1 1.1.1 Sets and Set Inclusion 1 1.1.2 Set Algebra 2 1.2 Single-Valued Functions 4 1.3 Real and Extended Real Numbers 6 1.4 Metric Spaces 7 1.5 Limits of Sequences 8 1.6 Point-Set Theory 10 1.7 Continuous Functions 12 1.8 Operations on Sequences of Sets 13 1.9 Classes of Subsets of Ω 15 1.9.1 Topological Space 15 1.9.2 σ-Algebra of Sets and the Borel σ-Algebra 15 1.10 Set and Measure Functions 17 1.10.1 Set Functions 17 1.10.2 Measure Functions 18 1.10.3 Outer Measure Functions 19 1.10.4 Complete Measure Functions 21 1.10.5 Lebesgue Measure 21 1.10.6 Measurable Functions 23 1.10.7 Lebesgue Measurable Functions 26 1.11 Normed Linear Spaces 27 1.11.1 Space of Bounded Real-Valued Functions 27 1.11.2 Space of Bounded Continuous Real-Valued Functions 28 1.11.3 Some Classical Banach Spaces 29 1.12 Integration 31 1.12.1 Integral of a Non-negative Simple Function 32 1.12.2 Integral of a Non-negative Measurable Function Using Simple Functions 33 1.12.3 Integral of a Measurable Function 33 1.12.4 Integral of a Measurable Function on a Measurable Set 34 1.12.5 Convergence of Sequences of Functions 35 2 Mathematical Foundations 2: Probability, Random Variables, and Convergence of Random Variables 37 2.1 Probability Spaces 37 2.2 Probability Distributions 42 2.3 The Expectation of a Random Variable 49 2.3.1 Theoretical Underpinnings 49 2.3.2 Computational Considerations 50 2.4 Moments of a Random Variable 52 2.5 Multiple Random Variables 54 2.5.1 The Discrete Case 54 2.5.2 The Continuous Case 59 2.5.3 Expectations and Moments 63 2.5.4 The Multivariate Discrete and Continuous Cases 69 2.6 Convergence of Sequences of Random Variables 72 2.6.1 Almost Sure Convergence 73 2.6.2 Convergence in Lp,p>0 73 2.6.3 Convergence in Probability 75 2.6.4 Convergence in Distribution 75 2.6.5 Convergence of Expectations 76 2.6.6 Convergence of Sequences of Events 78 2.6.7 Applications of Convergence of Random Variables 79 2.7 A Couple of Important Inequalities 80 Appendix 2.A The Conditional Expectation E(X|Y) 81 3 Mathematical Foundations 3: Stochastic Processes, Martingales, and Brownian Motion 85 3.1 Stochastic Processes 85 3.1.1 Finite-Dimensional Distributions of a Stochastic Process 86 3.1.2 Selected Characteristics of Stochastic Processes 88 3.1.3 Filtrations of A 89 3.2 Martingales 91 3.2.1 Discrete-Time Martingales 91 3.2.1.1 Discrete-Time Martingale Convergence 93 3.2.2 Continuous-Time Martingales 96 3.2.2.1 Continuous-Time Martingale Convergence 97 3.2.3 Martingale Inequalities 97 3.3 Path Regularity of Stochastic Processes 98 3.4 Symmetric Random Walk 99 3.5 Brownian Motion 100 3.5.1 Standard Brownian Motion 100 3.5.2 BM as a Markov Process 104 3.5.3 Constructing BM 106 3.5.3.1 BM Constructed from N(0, 1) Random Variables 106 3.5.3.2 BM as the Limit of Symmetric Random Walks 108 3.5.4 White Noise Process 109 Appendix 3.A Kolmogorov Existence Theorem: Another Look 109 Appendix 3.B Nondifferentiability of BM 110 4 Mathematical Foundations 4: Stochastic Integrals, Itô’s Integral, Itô’s Formula, and Martingale Representation 113 4.1 Introduction 113 4.2 Stochastic Integration: The Itô Integral 114 4.3 One-Dimensional Itô Formula 120 4.4 Martingale Representation Theorem 126 4.5 Multidimensional Itô Formula 127 Appendix 4.A Itô’s Formula 129 Appendix 4.B Multidimensional Itô Formula 130 5 Stochastic Differential Equations 133 5.1 Introduction 133 5.2 Existence and Uniqueness of Solutions 134 5.3 Linear SDEs 136 5.3.1 Strong Solutions to Linear SDEs 137 5.3.2 Properties of Solutions 147 5.3.3 Solutions to SDEs as Markov Processes 152 5.4 SDEs and Stability 154 Appendix 5.A Solutions of Linear SDEs in Product Form (Evans, 2013; Gard, 1988) 159 5.A.1 Linear Homogeneous Variety 159 5.A.2 Linear Variety 161 Appendix 5.B Integrating Factors and Variation of Parameters 162 5.B.1 Integrating Factors 163 5.B.2 Variation of Parameters 164 6 Stochastic Population Growth Models 167 6.1 Introduction 167 6.2 A Deterministic Population Growth Model 168 6.3 A Stochastic Population Growth Model 169 6.4 Deterministic and Stochastic Logistic Growth Models 170 6.5 Deterministic and Stochastic Generalized Logistic Growth Models 174 6.6 Deterministic and Stochastic Gompertz Growth Models 177 6.7 Deterministic and Stochastic Negative Exponential Growth Models 179 6.8 Deterministic and Stochastic Linear Growth Models 181 6.9 Stochastic Square-Root Growth Model with Mean Reversion 182 Appendix 6.A Deterministic and Stochastic Logistic Growth Models with an Allee Effect 184 Appendix 6.B Reducible SDEs 189 7 Approximation and Estimation of Solutions to Stochastic Differential Equations 193 7.1 Introduction 193 7.2 Iterative Schemes for Approximating SDEs 194 7.2.1 The EM Approximation 194 7.2.2 Strong and Weak Convergence of the EM Scheme 196 7.2.3 The Milstein (Second-Order) Approximation 196 7.3 The Lamperti Transformation 199 7.4 Variations on the EM and Milstein Schemes 203 7.5 Local Linearization Techniques 205 7.5.1 The Ozaki Method 205 7.5.2 The Shoji–Ozaki Method 207 7.5.3 The Rate of Convergence of the Local Linearization Method 211 Appendix 7.A Stochastic Taylor Expansions 212 Appendix 7.B The EM and Milstein Discretizations 217 7.B.1 The EM Scheme 217 7.B.2 The Milstein Scheme 218 Appendix 7.C The Lamperti Transformation 219 8 Estimation of Parameters of Stochastic Differential Equations 221 8.1 Introduction 221 8.2 The Transition Probability Density Function Is Known 222 8.3 The Transition Probability Density Function Is Unknown 227 8.3.1 Parameter Estimation via Approximation Methods 228 8.3.1.1 The EM Routine 228 8.3.1.2 The Ozaki Routine 230 8.3.1.3 The SO Routine 233 Appendix 8.A The ML Technique 235 Appendix 8.B The Log-Normal Probability Distribution 238 Appendix 8.C The Markov Property, Transitional Densities, and the Likelihood Function of the Sample 239 Appendix 8.D Change of Variable 241 Appendix A: A Review of Some Fundamental Calculus Concepts 245 Appendix B: The Lebesgue Integral 259 Appendix C: Lebesgue–Stieltjes Integral 261 Appendix D: A Brief Review of Ordinary Differential Equations 263 References 275 Index 279
£100.76
Springer-Verlag New York Inc. Stochastic Processes and Applications
Book SynopsisThis book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated.The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to Trade Review“This is another useful book for readers with ‘normal’ knowledge in mathematics, in particular in analysis, probability and partial differential equations. The goal of the author is to describe basic techniques from the theory of stochastic processes needed to answer questions coming from natural sciences such as physics and chemistry. … The book will be accessible and useful for graduate university students and teachers of courses in applied mathematics and other natural sciences.” (Jordan M. Stoyanov, zbMATH 1318.60003, 2015)"In the reviewer's opinion, [Stochastic Processes and Applications] could be recommended for ambitious undergraduate and standard graduate students as well as researchers who are unfamiliar with stochastic processes but eager to apply them to random phenomena, as a reference appropriate for use both as a textbook and for self-study."Isamu Doku, review for the American Mathematical SocietyTable of ContentsStochastic Processes.- Diffusion Processes.- Introduction to Stochastic Differential Equations.- The Fokker-Planck Equation.- Modelling with Stochastic Differential Equations.- The Langevin Equation.- Exit Problems for Diffusions.- Derivation of the Langevin Equation.- Linear Response Theory.- Appendix A Frequently Used Notations.- Appendix B Elements of Probability Theory.
£999.99
Springer-Verlag New York Inc. Free Probability and Random Matrices 35 Fields
Book SynopsisTrade Review“This book is an excellent survey, respectively introduction, into recent developments in free probability theory and its applications to random matrices. The authors superbly guide the reader through a number of important examples and present a carefully selected list of 207 relevant publications.” (Ludwig Paditz, zbMATH 1387.60005, 2018)Table of Contents1. Asymptotic Freeness of Gaussian Random Matrices.- 2. The Free Central Limit Theorem and Free Cumulants.- 3. Free Harmonic Analysis.- 4. Asymptotic Freeness.- 5. Second Order Freeness.- 6. Free Group Factors and Freeness.- 7. Free Entropy X-the Microstates Approach via Large Deviations.- Free Entropy X*-the Non-Microstates Approach via Free Fisher Information.- 9. Operator-Valued Free Probability Theory and Block Random Matrices.- 10. Polynomials in Free Variables and Operator-Valued Convolution.- 11. Brown Measure.- Solutions to Exercises.- References.- Index of Exercises.
£107.99
Centre for the Study of Language & Information Stochastic Causality
Book SynopsisThe papers collected here focus on probabilistic causality, addressing topics such as the search for causal mechanisms, epistemic and metaphysical views of causality, Bayesian nets and causal dependence, and causation in the special sciences. Some papers stress the statistical analysis of probabilistic data; others address causal issues in physics, with an emphasis on physical processes that are also probabilistic—i.e., stochastic processes.
£22.00
Society for Industrial & Applied Mathematics,U.S. Stochastic Processes, Estimation, and Control
Book SynopsisUncertainty and risk are integral to engineering because real systems have inherent ambiguities that arise naturally or due to our inability to model complex physics. The authors discuss probability theory, stochastic processes, estimation, and stochastic control strategies and show how probability can be used to model uncertainty in control and estimation problems. The material is practical and rich in research opportunities.The authors provide a comprehensive treatment of stochastic systems from the foundations of probability to stochastic optimal control. The book covers discrete- and continuous-time stochastic dynamic systems leading to the derivation of the Kalman filter, its properties, and its relation to the frequency domain Wiener filter as well as the dynamic programming derivation of the linear quadratic Gaussian (LQG) and the linear exponential Gaussian (LEG) controllers and their relation to H2 and H-inf controllers and system robustness.Stochastic Processes, Estimation, and Control is divided into three related sections. First, the authors present the concepts of probability theory, random variables, and stochastic processes, which lead to the topics of expectation, conditional expectation, and discrete-time estimation and the Kalman filter. After establishing this foundation, stochastic calculus and continuous-time estimation are introduced. Finally, dynamic programming for both discrete-time and continuous-time systems leads to the solution of optimal stochastic control problems, resulting in controllers with significant practical application.
£104.55
ISTE Ltd and John Wiley & Sons Inc Theory and Statistical Applications of Stochastic
Book SynopsisThis book is concerned with the theory of stochastic processes and the theoretical aspects of statistics for stochastic processes. It combines classic topics such as construction of stochastic processes, associated filtrations, processes with independent increments, Gaussian processes, martingales, Markov properties, continuity and related properties of trajectories with contemporary subjects: integration with respect to Gaussian processes, Itȏ integration, stochastic analysis, stochastic differential equations, fractional Brownian motion and parameter estimation in diffusion models. Table of ContentsPreface xi Introduction xiii Part 1 Theory of Stochastic Processes 1 Chapter 1 Stochastic Processes General Properties. Trajectories, Finite-dimensional Distributions 3 1.1 Definition of a stochastic process 3 1.2 Trajectories of a stochastic process Some examples of stochastic processes 5 1.2.1 Definition of trajectory and some examples 5 1.2.2 Trajectory of a stochastic process as a random element.8 1.3 Finite-dimensional distributions of stochastic processes: consistency conditions.10 1.3.1 Definition and properties of finite-dimensional distributions 10 1.3.2 Consistency conditions.11 1.3.3 Cylinder sets and generated σ-algebra 13 1.3.4 Kolmogorov theorem on the construction of a stochastic process by the family of probability distributions 15 1.4 Properties of σ-algebra generated by cylinder sets. The notion of σ-algebra generated by a stochastic process 19 Chapter 2 Stochastic Processes with Independent Increments 21 2.1 Existence of processes with independent increments in terms of incremental characteristic functions 21 2.2 Wiener process 24 2.2.1 One-dimensional Wiener process 24 2.2.2 Independent stochastic processes Multidimensional Wiener process 24 2.3 Poisson process 27 2.3.1 Poisson process defined via the existence theorem 27 2.3.2 Poisson process defined via the distributions of the increments 28 2.3.3 Poisson process as a renewal process 30 2.4 Compound Poisson process 33 2.5 Lévy processes 34 2.5.1 Wiener process with a drift 36 2.5.2 Compound Poisson process as a Lévy process 36 2.5.3 Sum of a Wiener process with a drift and a Poisson process 36 2.5.4 Gamma process 37 2.5.5 Stable Lévy motion37 2.5.6 Stable Lévy subordinator with stability parameter α ∈ (0, 1) 38 Chapter 3 Gaussian Processes Integration with Respect to Gaussian Processes 39 3.1 Gaussian vectors 39 3.2 Theorem of Gaussian representation (theorem on normal correlation) 42 3.3 Gaussian processes. 44 3.4 Examples of Gaussian processes 46 3.4.1 Wiener process as an example of a Gaussian process 46 3.4.2 Fractional Brownian motion.48 3.4.3 Sub-fractional and bi-fractional Brownian motion 50 3.4.4 Brownian bridge 50 3.4.5 Ornstein–Uhlenbeck process 51 3.5 Integration of non-random functions with respect to Gaussian processes 52 3.5.1 General approach 52 3.5.2 Integration of non-random functions with respect to the Wiener process 54 3.5.3 Integration w.r.t the fractional Brownian motion 57 3.6 Two-sided Wiener process and fractional Brownian motion: Mandelbrot–van Ness representation of fractional Brownian motion 60 3.7 Representation of fractional Brownian motion as the Wiener integral on the compact integral 63 Chapter 4 Construction, Properties and Some Functionals of the Wiener Process and Fractional Brownian Motion 67 4.1 Construction of a Wiener process on the interval [0, 1] 67 4.2 Construction of a Wiener process on R+ 72 4.3 Nowhere differentiability of the trajectories of a Wiener process 74 4.4 Power variation of the Wiener process and of the fractional Brownian motion77 4.4.1 Ergodic theorem for power variations 77 4.5 Self-similar stochastic processes 79 4.5.1 Definition of self-similarity and some examples 79 4.5.2 Power variations of self-similar processes on finite intervals.80 Chapter 5 Martingales and Related Processes 85 5.1 Notion of stochastic basis with filtration 85 5.2 Notion of (sub-, super-) martingale: elementary properties 86 5.3 Examples of (sub-, super-) martingales 87 5.4 Markov moments and stopping times 90 5.5 Martingales and related processes with discrete time 96 5.5.1 Upcrossings of the interval and existence of the limit of submartingale 96 5.5.2 Examples of martingales having a limit and of uniformly and non-uniformly integrable martingales 102 5.5.3 Lévy convergence theorem 104 5.5.4 Optional stopping 105 5.5.5 Maximal inequalities for (sub-, super-) martingales 108 5.5.6 Doob decomposition for the integrable processes with discrete time 111 5.5.7 Quadratic variation and quadratic characteristics: Burkholder–Davis–Gundy inequalities 113 5.5.8 Change of probability measure and Girsanov theorem for discrete-time processes 116 5.5.9 Strong law of large numbers for martingales with discrete time 120 5.6 Lévy martingale stopped 126 5.7 Martingales with continuous time 127 Chapter 6 Regularity of Trajectories of Stochastic Processes 131 6.1 Continuity in probability and in L2(Ω,F, P) 131 6.2 Modification of stochastic processes: stochastically equivalent and indistinguishable processes 133 6.3 Separable stochastic processes: existence of separable modification 135 6.4 Conditions of D-regularity and absence of the discontinuities of the second kind for stochastic processes 138 6.4.1 Skorokhod conditions of D-regularity in terms of three-dimensional distributions 138 6.4.2 Conditions of absence of the discontinuities of the second kind formulated in terms of conditional probabilities of large increments 144 6.5 Conditions of continuity of trajectories of stochastic processes 148 6.5.1 Kolmogorov conditions of continuity in terms of two-dimensional distributions 148 6.5.2 Hölder continuity of stochastic processes: a sufficient condition 152 6.5.3 Conditions of continuity in terms of conditional probabilities 154 Chapter 7 Markov and Diffusion Processes 157 7.1 Markov property 157 7.2 Examples of Markov processes 163 7.2.1 Discrete-time Markov chain 163 7.2.2 Continuous-time Markov chain 165 7.2.3 Process with independent increments 168 7.3 Semigroup resolvent operator and generator related to the homogeneous Markov process 168 7.3.1 Semigroup related to Markov process 168 7.3.2 Resolvent operator and resolvent equation 169 7.3.3 Generator of a semigroup.171 7.4 Definition and basic properties of diffusion process 175 7.5 Homogeneous diffusion process Wiener process as a diffusion process 179 7.6 Kolmogorov equations for diffusions 181 Chapter 8 Stochastic Integration 187 8.1 Motivation..187 8.2 Definition of Itô integral 189 8.2.1 Itô integral of Wiener process 195 8.3 Continuity of Itô integral 197 8.4 Extended Itô integral 199 8.5 Itô processes and Itô formula 203 8.6 Multivariate stochastic calculus 212 8.7 Maximal inequalities for Itô martingales 215 8.7.1 Strong law of large numbers for Itô local martingales 218 8.8 Lévy martingale characterization of Wiener process 220 8.9 Girsanov theorem 223 8.10 Itô representation 228 Chapter 9 Stochastic Differential Equations.233 9.1 Definition, solvability conditions, examples 233 9.1.1 Existence and uniqueness of solution 234 9.1.2 Some special stochastic differential equations 238 9.2 Properties of solutions to stochastic differential equations 241 9.3 Continuous dependence of solutions on coefficients 245 9.4 Weak solutions to stochastic differential equations. 247 9.5 Solutions to SDEs as diffusion processe 249 9.6 Viability, comparison and positivity of solutions to stochastic differential equations 252 9.6.1 Comparison theorem for one-dimensional projections of stochastic differential equations 257 9.6.2 Non-negativity of solutions to stochastic differential equations 258 9.7 Feynman–Kac formula 258 9.8 Diffusion model of financial markets 260 9.8.1 Admissible portfolios, arbitrage and equivalent martingale measure 263 9.8.2 Contingent claims, pricing and hedging 266 Part 2 Statistics of Stochastic Processes 271 Chapter 10 Parameter Estimation 273 10.1 Drift and diffusion parameter estimation in the linear regression model with discrete time 273 10.1.1 Drift estimation in the linear regression model with discrete time in the case when the initial value is known 274 10.1.2 Drift estimation in the case when the initial value is unknown 277 10.2 Estimation of the diffusion coefficient in a linear regression model with discrete time 277 10.3 Drift and diffusion parameter estimation in the linear model with continuous time and the Wiener noise 278 10.3.1 Drift parameter estimation 279 10.3.2 Diffusion parameter estimation 280 10.4 Parameter estimation in linear models with fractional Brownian motion 281 10.4.1 Estimation of Hurst index 281 10.4.2 Estimation of the diffusion parameter 283 10.5 Drift parameter estimation 284 10.6 Drift parameter estimation in the simplest autoregressive model 285 10.7 Drift parameters estimation in the homogeneous diffusion model 289 Chapter 11 Filtering Problem Kalman-Bucy Filter 293 11.1 General setting 293 11.2 Auxiliary properties of the non-observable process 294 11.3 What is an optimal filter 295 11.4 Representation of an optimal filter via an integral equation with respect to an observable process 296 11.5 Integral Wiener-Hopf equation 299 Appendices 311 Appendix 1 313 Appendix 2 329 Bibliography 363 Index 369
£125.06
ISTE Ltd and John Wiley & Sons Inc Discrete Time Branching Processes in Random
Book SynopsisBranching processes are stochastic processes which represent the reproduction of particles, such as individuals within a population, and thereby model demographic stochasticity. In branching processes in random environment (BPREs), additional environmental stochasticity is incorporated, meaning that the conditions of reproduction may vary in a random fashion from one generation to the next. This book offers an introduction to the basics of BPREs and then presents the cases of critical and subcritical processes in detail, the latter dividing into weakly, intermediate, and strongly subcritical regimes.Table of Contents1. Branching Processes in Varying Environment. 2. Branching Processes in Random Environment. 3. Large Deviations for BPREs. 4. Properties of Random Walks. 5. Critical BPREs: the Annealed Approach. 6. Critical BPREs: the Quenched Approach. 7. Weakly Subcritical BPREs. 8. Intermediate Subcritical BPREs. 9. Strongly Subcritical BPREs. 10. Multi-type BPREs.
£125.06
ISTE Ltd and John Wiley & Sons Inc Introduction to Stochastic Processes and
Book SynopsisMastering chance has, for a long time, been a preoccupation of mathematical research. Today, we possess a predictive approach to the evolution of systems based on the theory of probabilities. Even so, uncovering this subject is sometimes complex, because it necessitates a good knowledge of the underlying mathematics. This book offers an introduction to the processes linked to the fluctuations in chance and the use of numerical methods to approach solutions that are difficult to obtain through an analytical approach. It takes classic examples of inventory and queueing management, and addresses more diverse subjects such as equipment reliability, genetics, population dynamics, physics and even market finance. It is addressed to those at Master�s level, at university, engineering school or management school, but also to an audience of those in continuing education, in order that they may discover the vast field of decision support.Table of ContentsPart 1. Basic Mathematical Concepts 1. Basic Reminders of Probability. 2. Probabilistic Models. 3. Inventory Management. Part 2. Stochastic Processes 4. Markov Chains. 5. Markov Processes. 6. Queueing Systems. 7. Various Applications. Part 3. Simulation 8. Generator Programs. 9. Principles of Simulation. 10. Simulation of Inventory Management. 11. Simulation of a Queueing Process. 12. Optimization and Simulation.
£125.06
ISTE Ltd and John Wiley & Sons Inc Introduction to Matrix Analytic Methods in Queues
Book SynopsisMatrix-analytic methods (MAM) were introduced by Professor Marcel Neuts and have been applied to a variety of stochastic models since. In order to provide a clear and deep understanding of MAM while showing their power, this book presents MAM concepts and explains the results using a number of worked-out examples.This book’s approach will inform and kindle the interest of researchers attracted to this fertile field. To allow readers to practice and gain experience in the algorithmic and computational procedures of MAM, Introduction to Matrix Analytic Methods in Queues 1 provides a number of computational exercises. It also incorporates simulation as another tool for studying complex stochastic models, especially when the state space of the underlying stochastic models under analytic study grows exponentially.The book’s detailed approach will make it more accessible for readers interested in learning about MAM in stochastic models.Table of ContentsList of Notations ix Preface xi Chapter 1 Introduction 1 1.1. Probability concepts 2 1.1.1. Random variables 5 1.1.2. Discrete probability functions 6 1.1.3. Probability generating function 7 1.1.4. Continuous probability functions 7 1.1.5. Laplace transform and Laplace-Stieltjes transform 9 1.1.6. Measures of a random variable 10 1.2. Renewal process 11 1.2.1. Renewal function 12 1.2.2. Terminating renewal process 15 1.2.3. Poisson process 16 1.3. Matrix analysis 18 1.3.1. Basics 18 1.3.2. Eigenvalues and eigenvectors 23 1.3.3. Partitioned matrices 27 1.3.4. Matrix differentiation 28 1.3.5. Exponential matrix 30 1.3.6. Kronecker products and Kronecker sums 32 1.3.7. Vectorization (or direct sums) of matrices 33 Chapter 2 Markov Chains 35 2.1. Discrete-time Markov chains (DTMC) 36 2.1.1. Basic concepts, key definitions and results 36 2.1.2. Computation of the steady-state probability vector of DTMC 43 2.1.3. Absorbing DTMC 45 2.1.4. Taboo probabilities in DTMC 47 2.2. Continuous-time Markov chain (CTMC) 48 2.2.1. Basic concepts, key definitions and results 48 2.2.2. Computation of exponential matrix 52 2.2.3. Computation of the limiting probabilities of CTMC 57 2.2.4. Computation of the mean first passage times 58 2.3. Semi-Markov and Markov renewal processes 61 Chapter 3 Discrete Phase Type Distributions 71 3.1. Discrete phase type (DPH) distribution 72 3.2. DPH renewal processes 92 3.3. Exercises 97 Chapter 4 Continuous Phase Type Distributions 101 4.1. Continuous phase type (CPH) distribution 101 4.2. CPH renewal process 120 4.3. Exercises 137 Chapter 5 Discrete-Batch Markovian Arrival Process 143 5.1. Discrete-batch Markovian arrival process (D-BMAP) 144 5.2. Counting process associated with the D-BMAP 152 5.3. Generation of D-MAP processes for numerical purposes 162 5.4. Exercises 165 Chapter 6 Continuous-Batch Markovian Arrival Process 171 6.1. Continuous-time batch Markovian arrival process (BMAP) 171 6.2. Counting processes associated with BMAP 177 6.3. Generation of MAP processes for numerical purposes 198 6.4. Exercises 206 Chapter 7 Matrix-Analytic Methods (Discrete-Time) 213 7.1. M/G/1-paradigm (scalar case) 215 7.2. M/G/1-paradigm (matrix case) 224 7.3. GI/M/1-paradigm (scalar case) 244 7.4. GI/M/1-paradigm (matrix case) 252 7.5. QBD process (scalar case) 268 7.6. QBD process (matrix case) 269 7.7. Exercises 278 Chapter 8. Matrix-Analytic Methods (Continuous-time) 291 8.1. M/G/1-type (scalar case) 291 8.2. M/G/1-type (matrix case) 295 8.3. GI/M/1-type (scalar case) 297 8.4. GI/M/1-type (matrix case) 300 8.5. QBD process (scalar case) 304 8.6. QBD process (matrix case) 305 8.7. Exercises 308 Chapter 9. Applications 321 9.1. Production and manufacturing 322 9.2. Service sectors 323 9.2.1. Healthcare 324 9.2.2. Artificial Intelligence and the Internet of Things 324 9.2.3. Biological and medicine 325 9.2.4. Telecommunications 325 9.2.5. Supply chain 325 9.2.6. Consumer issues 326 References 327 Index 335 Summary of Volume 2 339
£112.50
ISTE Ltd and John Wiley & Sons Inc Applied Diffusion Processes from Engineering to
Book SynopsisThe aim of this book is to promote interaction between engineering, finance and insurance, as these three domains have many models and methods of solution in common for solving real-life problems. The authors point out the strict inter-relations that exist among the diffusion models used in engineering, finance and insurance. In each of the three fields, the basic diffusion models are presented and their strong similarities are discussed. Analytical, numerical and Monte Carlo simulation methods are explained with a view to applying them to obtain the solutions to the different problems presented in the book. Advanced topics such as nonlinear problems, Lévy processes and semi-Markov models in interactions with the diffusion models are discussed, as well as possible future interactions among engineering, finance and insurance. Contents 1. Diffusion Phenomena and Models.2. Probabilistic Models of Diffusion Processes.3. Solving Partial Differential Equations of Second Order.4. Problems in Finance.5. Basic PDE in Finance.6. Exotic and American Options Pricing Theory.7. Hitting Times for Diffusion Processes and Stochastic Models in Insurance.8. Numerical Methods.9. Advanced Topics in Engineering: Nonlinear Models.10. Lévy Processes.11. Advanced Topics in Insurance: Copula Models and VaR Techniques.12. Advanced Topics in Finance: Semi-Markov Models.13. Monte Carlo Semi-Markov Simulation Methods.Table of ContentsIntroduction xiii Chapter 1 Diffusion Phenomena and Models 1 1.1 General presentation of diffusion process 1 1.2 General balance equations 6 1.3 Heat conduction equation 10 1.4 Initial and boundary conditions 12 Chapter 2 Probabilistic Models of Diffusion Processes 17 2.1 Stochastic differentiation 17 2.2 Itô’s formula 19 2.3 Stochastic differential equations (SDE) 24 2.4 Itô and diffusion processes 28 2.5 Some particular cases of diffusion processes 32 2.6 Multidimensional diffusion processes 36 2.7 The Stroock–Varadhan martingale characterization of diffusions (Karlin and Taylor) 41 2.8 The Feynman–Kac formula (Platen and Heath) 42 Chapter 3 Solving Partial Differential Equations of Second Order 47 3.1 Basic definitions on PDE of second order 47 3.2 Solving the heat equation 51 3.3 Solution by the method of Laplace transform 65 3.4 Green’s functions 75 Chapter 4 Problems in Finance 85 4.1 Basic stochastic models for stock prices 85 4.2 The bond investments 90 4.3 Dynamic deterministic continuous time model for instantaneous interest rate 93 4.4 Stochastic continuous time dynamic model for instantaneous interest rate 98 4.5 Multidimensional Black and Scholes model 110 Chapter 5 Basic PDE in Finance 111 5.1 Introduction to option theory 111 5.2 Pricing the plain vanilla call with the Black–Scholes–Samuelson model 115 5.3 Pricing no plain vanilla calls with the Black-Scholes-Samuelson model 120 5.4 Zero-coupon pricing under the assumption of no arbitrage 127 Chapter 6 Exotic and American Options Pricing Theory 145 6.1 Introduction 145 6.2 The Garman–Kohlhagen formula 146 6.3 Binary or digital options 149 6.4 “Asset or nothing” options 150 6.5 Numerical examples 152 6.6 Path-dependent options 153 6.7 Multi-asset options 157 6.8 American options 165 Chapter 7 Hitting Times for Diffusion Processes and Stochastic Models in Insurance 177 7.1 Hitting or first passage times for some diffusion processes 177 7.2 Merton’s model for default risk 193 7.3 Risk diffusion models for insurance 201 Chapter 8 Numerical Methods 219 8.1 Introduction 219 8.2 Discretization and numerical differentiation 220 8.3 Finite difference methods 222 9.1 Nonlinear model in heat conduction 232 Chapter 9 Advanced Topics in Engineering: Nonlinear Models 231 9.2 Integral method applied to diffusive problems 233 9.3 Integral method applied to nonlinear problems 239 9.4 Use of transformations in nonlinear problems 243 Chapter 10 Lévy Processes 255 10.1 Motivation 255 10.2 Notion of characteristic functions 257 10.3 Lévy processes 257 10.4 Lévy–Khintchine formula 259 10.5 Examples of Lévy processes 261 10.6 Variance gamma (VG) process 264 10.7 The Brownian–Poisson model with jumps 266 10.8 Risk neutral measures for Lévy models in finance 275 10.9 Conclusion 276 Chapter 11 Advanced Topics in Insurance: Copula Models and VaR Techniques 277 11.1 Introduction 277 11.2 Sklar theorem (1959) 279 11.3 Particular cases and Fréchet bounds 280 11.4 Dependence 288 11.5 Applications in finance: pricing of the bivariate digital put option 293 11.6 VaR application in insurance 296 Chapter 12 Advanced Topics in Finance: Semi-Markov Models 307 12.1 Introduction 307 12.2 Homogeneous semi-Markov process 308 12.3 Semi-Markov option model 328 12.4 Semi-Markov VaR models 332 12.5 Conclusion 339 Chapter 13 Monte Carlo Semi-Markov Simulation Methods 341 13.1 Presentation of our simulation model 341 13.2 The semi-Markov Monte Carlo model in a homogeneous environment 345 13.3 A credit risk example 350 13.4 Semi-Markov Monte Carlo with initial recurrence backward time in homogeneous case 362 13.5 The SMMC applied to claim reserving problem 363 13.6 An example of claim reserving calculation 366 Conclusion 379 Bibliography 381 Index 393
£150.26
Edward Elgar Publishing Ltd Nonlinear Economic Models: Cross-sectional, Time
Book SynopsisNonlinear modelling has become increasingly important and widely used in economics. This valuable book brings together recent advances in the area including contributions covering cross-sectional studies of income distribution and discrete choice models, time series models of exchange rate dynamics and jump processes, and artificial neural network and genetic algorithm models of financial markets. Attention is given to the development of theoretical models as well as estimation and testing methods with a wide range of applications in micro and macroeconomics, labour and finance.The book provides valuable introductory material that is accessible to students and scholars interested in this exciting research area, as well as presenting the results of new and original research. Nonlinear Economic Models provides a sequel to Chaos and Nonlinear Models in Economics by the same editors.Trade Review'This collection provides valuable introductory material that is accessible to students and scholars interested in this research area.' -- Business HorizonsTable of ContentsContents: Part I: Introduction 1. Nonlinear Modelling: An Introduction Part II: Cross-sectional Applications 2. A Model of Income Distribution 3. Truncated Distribution Families 4. Betit: A Flexible Binary Choice Model 5. Estimation of Generalised Distributions 6. Age and the Distribution of Earnings 7. Count Data and Discrete Distributions Part III: Time Series Applications 8. A Model of the Real Exchange Rate 9. Jump Models and Higher Moments 10. A Topological Test of Chaos 11. Genetic Algorithms and Trading Rules Part IV: Neural Network Applications 12. Artificial Neural Networks 13. An ANN Model of the Stock Market 14. Exchange Rate Forecasting Models Index
£111.00
Springer Nature Switzerland AG The Theory of Queuing Systems with Correlated Flows
Book SynopsisThis book is dedicated to the systematization and development of models, methods, and algorithms for queuing systems with correlated arrivals. After first setting up the basic tools needed for the study of queuing theory, the authors concentrate on complicated systems: multi-server systems with phase type distribution of service time or single-server queues with arbitrary distribution of service time or semi-Markovian service. They pay special attention to practically important retrial queues, tandem queues, and queues with unreliable servers. Mathematical models of networks and queuing systems are widely used for the study and optimization of various technical, physical, economic, industrial, and administrative systems, and this book will be valuable for researchers, graduate students, and practitioners in these domains.Trade Review“The book fills a unique void and is a welcome addition to the queueing literature. The writing style is friendly and accessible, and the authors are to be congratulated on their accomplishment.” (Myron Hlynka, Mathematical Reviews, April, 2021)Table of ContentsMathematical Methods to Study Classical Queuing Systems.- Methods to Study Queuing Systems with Correlated Arrivals.- Queuing Systems with Waiting Space and Correlated Arrivals and Their Application to Evaluation of Network Structure Performance.- Retrial Queuing Systems with Correlated Input Flows and Their Application for Network Structures Performance Evaluation.- Mathematical Models and Methods of Investigation of Hybrid Communication Networks Based on Laser and Radio Technologies.- Tandem Queues with Correlated Arrivals and Their Application to System Structure Performance Evaluation.- App. A, Some Information from the Theory of Matrices and Functions of Matrices.
£80.99
Springer Nature Switzerland AG Stochastik 2: Von der Standardabweichung bis zur
Book SynopsisAufbauend auf dem ersten Band, werden in diesem Buch weiterführende Konzepte der Wahrscheinlichkeitstheorie ausführlich und verständlich diskutiert. Mit vielen exemplarisch durchgerechneten Aufgaben, einer Vielzahl weiterer Problemstellungen und ausführlichen Lösungen bietet es dem Leser die Möglichkeit, die eigenen Fähigkeiten ständig zu erweitern und kritisch zu überprüfen und ein tieferes Verständnis der Materie zu erlangen. Realitätsnahe Anwendungen ermöglichen einen Ausblick in die breite Verwendbarkeit dieser Theorie.Auch in diesem Band wird auf die Entwicklung der Begriffsbildung und der mathematischen Konzepte besonderer Wert gelegt, sodass man ihre Bedeutung bei der Erzeugung wie auch ständige Verbesserung von Forschungsinstrumenten für die Untersuchung unserer Welt erleben kann. Gerichtet ist das Buch an Gymnasiasten, Studienanfänger an Hochschulen, Lehrer und Interessierte, die sich mit diesem Gebiet vertraut machen möchten. Table of ContentsEinleitung.- Standardabweichung.- Wahrscheinlichkeiten von Wertebereichen.- Das Gesetz der grossen Zahlen.- Stetige Zufallsvariablen.- Erwartungswert und Standardabweichung von stetigen Zufallsvariablen.- Modellieren von Umfragen.- Hypothesentests.- Lineare Regression.
£26.59
Springer Nature Switzerland AG Concentration of Maxima and Fundamental Limits in
Book SynopsisThis book provides a unified exposition of some fundamental theoretical problems in high-dimensional statistics. It specifically considers the canonical problems of detection and support estimation for sparse signals observed with noise. Novel phase-transition results are obtained for the signal support estimation problem under a variety of statistical risks. Based on a surprising connection to a concentration of maxima probabilistic phenomenon, the authors obtain a complete characterization of the exact support recovery problem for thresholding estimators under dependent errors. Table of Contents
£49.49
Springer Nature Switzerland AG Optimal Control of Dynamic Systems Driven by
Book SynopsisThis book is devoted to the development of optimal control theory for finite dimensional systems governed by deterministic and stochastic differential equations driven by vector measures. The book deals with a broad class of controls, including regular controls (vector-valued measurable functions), relaxed controls (measure-valued functions) and controls determined by vector measures, where both fully and partially observed control problems are considered. In the past few decades, there have been remarkable advances in the field of systems and control theory thanks to the unprecedented interaction between mathematics and the physical and engineering sciences. Recently, optimal control theory for dynamic systems driven by vector measures has attracted increasing interest. This book presents this theory for dynamic systems governed by both ordinary and stochastic differential equations, including extensive results on the existence of optimal controls and necessary conditions for optimality. Computational algorithms are developed based on the optimality conditions, with numerical results presented to demonstrate the applicability of the theoretical results developed in the book. This book will be of interest to researchers in optimal control or applied functional analysis interested in applications of vector measures to control theory, stochastic systems driven by vector measures, and related topics. In particular, this self-contained account can be a starting point for further advances in the theory and applications of dynamic systems driven and controlled by vector measures.Trade Review“This book is a masterpiece of mathematical work where the authors joyfully stroll with the reader through the pleasant universe of control theory and its many applications. … I think the authors did a very good job. Their contribution is surely going to be particularly helpful to applied mathematicians. It’s a must read!” (Calvin Tadmon, SIAM Review, Vol. 64 (4), December, 2022)Table of Contents1 Mathematical Preliminaries.- 2 Linear Systems.- 3 Nonlinear Systems.- 4 Optimal Control: Existence Theory.- Optimal Control: Necessary Conditions of Optimality.- 6 Stochastic Systems Controlled by Vector Measures.- 7 Applications to Physical Examples.- Bibliography.- Index.
£98.99
Springer Nature Switzerland AG Methodology and Applications of Statistics: A
Book SynopsisDedicated to one of the most outstanding researchers in the field of statistics, this volume in honor of C.R. Rao, on the occasion of his 100th birthday, provides a bird’s-eye view of a broad spectrum of research topics, paralleling C.R. Rao’s wide-ranging research interests. The book’s contributors comprise a representative sample of the countless number of researchers whose careers have been influenced by C.R. Rao, through his work or his personal aid and advice. As such, written by experts from more than 15 countries, the book’s original and review contributions address topics including statistical inference, distribution theory, estimation theory, multivariate analysis, hypothesis testing, statistical modeling, design and sampling, shape and circular analysis, and applications. The book will appeal to statistics researchers, theoretical and applied alike, and PhD students. Happy Birthday, C.R. Rao!Table of ContentsPreface.- Dedication.- Part I – Inference.- Robust Statistical Inference for One-shot Devices Based on Density Power Divergences: An Overview (N. Balakrishnan, E. Castilla, L. Pardo).- Statistical Meaning of Mean Functions: A Novel Matrix Mean Derived from Fisher Information, authors: A.M. Kagan, P.J. Smith).- The Legend of the Equality of OLSE and BLUE: highlighted by C.R. Rao in 1967 (A. Markiewicz, S. Puntanen, G.P.H. Styan).- Comparison of Local Powers of Some Exact Tests for a Common Normal Mean with Unequal Variances (Y.G. Kifle, A.M. Moluh, B.K. Sinha).- Quantile Function: Overview of Collaboration with Professor C. R. Rao (G.J. Babu).- Part II – Distribution Theory.- Some Bivariate and Multivariate Models Involving Independent Gamma Distributed Components (B.C. Arnold).- An Absolute Continuous Bivariate Inverse Generalized Exponential Distribution: Properties, Inference and Extensions (D. Kundu).- Part III – Multivariate Analysis.- The Likelihood Ratio Test of Equality of Mean Vectors with a Doubly Exchangeable Covariance Matrix (C.A. Coelho, J. Pielaszkiewicz).- Bilinear Regression with Rank Restrictions on the Mean and the Dispersion Matrix (D. von Rosen).- Limiting Canonical Distribution of Two Large Dimensional Random Vectors (Z. Bai, Z. Hou, J. Hu, D. Jiang, X. Zhang).- Some Contributions to Multivariate Analysis due to C. R. Rao and Associated Developments (Y. Fujikoshi).- On Testing Structures of the Covariance Matrix: A Non-normal Approach (T. Kollo, M. Valge).- Part IV – Design and Sampling.- The Existence of Perpendicular Multi-arrays (K. Matsubara, S. Kageyama).- Statistical Design Issues for fMRI Studies: A Beginner’s Training Manual (B.K. Sinha, N.K. Mandal, M. Pal).- A Review of Rigorous Randomized Response Methods for Protecting Respondent's Privacy and Data Confidentiality (T. Nayak).- Part V – Shape and Circular Analysis.- A Statistical Analysis of the Cardioid Radial Growth Model (J.T. Kent, K.V. Mardia, L. Ippoliti, P. Valentini).- A Flexible Family of Mixed Distributions for Discrete Linear and Continuous Circular Random Variables (A. SenGupta, K. Shimizu, S.H. Ong, R. Das).- Goodness of Fit for Wrapped Stable Distributions Based on the Characteristic Function (S.G. Meintanis, S.R. Jammalamadaka, Q. Jin).- Part VI – Applications.- Partial Differential Equations Models and Riemann-Stieltjes Integrals in Measuring Sustainability (A.S.R.S. Rao, S. Saride).- Extreme Point Methodology in Power Calculations – The Case of Hardy-Weinberg Equilibrium (S. Venkatesan, M.B. Rao, H.-I. Hsiao).- Part VII – General.- On the Association of Professor C. R. Rao with the Poznan School of Mathematical Statistics and Biometry (T.Calinski).
£132.99
