Probability and statistics Books

Book SynopsisChapter 1 Bayesian and Frequentist Approaches in Infectious Disease Data Analysis.- Chapter 2 Generalized Linear Models in Infectious Disease Analysis and Surveillance: Methods for Independent Data.- Chapter 3 Variable Selection in Generalized Linear Models.- Chapter 4 Machine Learning Models for Probabilistic Inference and Prediction.- Chapter 5 Generalized Linear Models in Infectious Disease Analysis and Surveillance: Methods for Correlated Data.- Chapter 6 Residuals and Overdispersion in Generalized Linear Models.- Chapter 7 Interrupted Time Series Model in Infectious Disease Research and Surveillance.- Chapter 8 Generalized Linear Models with Missing Data.

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Book SynopsisThis book is a translation of the third edition of the well accepted German textbook 'Stochastik', which presents the fundamental ideas and results of both probability theory and statistics, and comprises the material of a one-year course. The stochastic concepts, models and methods are motivated by examples and problems and then developed and analysed systematically.Trade Review"The book can be used by undergraduate mathematics majors but also by science and engeneering students who wish not only to apply probability and statistics but also to understand how the methods work."Vladimir P. Kurenok in: Mathematical Reviews 2009b "The book is well-written and mathematically oriented students and researchers will certainly find that it provides a high level introduction to probability theory and mathematical statistics."In: EMS Newsletter 9/2008

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Book SynopsisIn the two-volume set ‘A Selection of Highlights’ we present basics of mathematics in an exciting and pedagogically sound way. This volume examines many fundamental results in Geometry and Discrete Mathematics along with their proofs and their history. In the second edition we include a new chapter on Topological Data Analysis and enhanced the chapter on Graph Theory for solving further classical problems such as the Traveling Salesman Problem.

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Book SynopsisThe present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order to study convergence to equilibrium, spectral bounds, functional inequalities such as Poincaré, Sobolev or logarithmic Sobolev inequalities, and various bounds on solutions of evolution equations. At the same time, it covers a large class of evolution and partial differential equations. The book is intended to serve as an introduction to the subject and to be accessible for beginning and advanced scientists and non-specialists. Simultaneously, it covers a wide range of results and techniques from the early developments in the mid-eighties to the latest achievements. As such, students and researchers interested in the modern aspects of Markov diffusion operators and semigroups and their connections to analytic functional inequalities, probabilistic convergence to equilibrium and geometric curvature will find it especially useful. Selected chapters can also be used for advanced courses on the topic.Trade Review“The book is friendly written and is of a rich content. With simple examples, main ideas of the study are clearly explained and naturally extended to a general framework, so that main progress in the field made for the past decades is presented in a smooth way. The monograph is undoubtedly a significant reference for further development of diffusion semigroups and related topics.” (Feng-Yu Wang, zbMATH 1376.60002, 2018)“It is extremely rich. It is more original and inspirational than a treatise. One can use it and benefit from it in many ways: as a reference book, as an inspiration source, by focusing on a property or on an example. … From the beginning to the end, this book definitely has a strong personality and a characteristic taste. … anybody who wants to explore analytic, probabilistic or geometric properties of Markov semigroups to have a look at it first.” (Thierry Coulhon, Jahresbericht der Deutschen Math-Vereinigung, Vol. 119, 2017)“This impressive monograph is about an important and highly active area that straddles the fertile land occupied by both probability and analysis. … It is written with great clarity and style, and was clearly a labour of love for the authors. I am convinced that it will be a valuable resource for researchers in analysis and probability for many years to come.” (David Applebaum, The Mathematical Gazette, Vol. 100 (548), July, 2016)Table of ContentsIntroduction.- Part I Markov semigroups, basics and examples: 1.Markov semigroups.- 2.Model examples.- 3.General setting.- Part II Three model functional inequalities: 4.Poincaré inequalities.- 5.Logarithmic Sobolev inequalities.- 6.Sobolev inequalities.- Part III Related functional, isoperimetric and transportation inequalities: 7.Generalized functional inequalities.- 8.Capacity and isoperimetry-type inequalities.- 9.Optimal transportation and functional inequalities.- Part IV Appendices: A.Semigroups of bounded operators on a Banach space.- B.Elements of stochastic calculus.- C.Some basic notions in differential and Riemannian geometry.- Notations and list of symbols.- Bibliography.- Index.

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Book SynopsisA certain curious feature of random objects, introduced by the author as “super concentration,” and two related topics, “chaos” and “multiple valleys,” are highlighted in this book. Although super concentration has established itself as a recognized feature in a number of areas of probability theory in the last twenty years (under a variety of names), the author was the first to discover and explore its connections with chaos and multiple valleys. He achieves a substantial degree of simplification and clarity in the presentation of these findings by using the spectral approach.Understanding the fluctuations of random objects is one of the major goals of probability theory and a whole subfield of probability and analysis, called concentration of measure, is devoted to understanding these fluctuations. This subfield offers a range of tools for computing upper bounds on the orders of fluctuations of very complicated random variables. Usually, concentration of measure is useful when more direct problem-specific approaches fail; as a result, it has massively gained acceptance over the last forty years. And yet, there is a large class of problems in which classical concentration of measure produces suboptimal bounds on the order of fluctuations. Here lies the substantial contribution of this book, which developed from a set of six lectures the author first held at the Cornell Probability Summer School in July 2012.The book is interspersed with a sizable number of open problems for professional mathematicians as well as exercises for graduate students working in the fields of probability theory and mathematical physics. The material is accessible to anyone who has attended a graduate course in probability.Table of ContentsPreface.- 1.Introduction.- 2.Markov semigroups.- 3.Super concentration and chaos.- 4.Multiple valleys.- 5.Talagrand’s method for proving super concentration.- 6.The spectral method for proving super concentration.- 7.Independent flips.- 8.Extremal fields.- 9.Further applications of hypercontractivity.- 10.The interpolation method for proving chaos.- 11.Variance lower bounds.- 12.Dimensions of level sets.- Appendix A. Gaussian random variables.- Appendix B. Hypercontractivity.- Bibliography.- Indices.

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Book SynopsisThis research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations (PDEs), and financial mathematics. It pays special attention to the relations between SDEs/BSDEs and second order PDEs under minimal regularity assumptions, and also extends those results to equations with multivalued coefficients. The authors present in particular the theory of reflected SDEs in the above mentioned framework and include exercises at the end of each chapter.Stochastic calculus and stochastic differential equations (SDEs) were first introduced by K. Itô in the 1940s, in order to construct the path of diffusion processes (which are continuous time Markov processes with continuous trajectories taking their values in a finite dimensional vector space or manifold), which had been studied from a more analytic point of view by Kolmogorov in the 1930s. Since then, this topic has become an important subject of Mathematics and Applied Mathematics, because of its mathematical richness and its importance for applications in many areas of Physics, Biology, Economics and Finance, where random processes play an increasingly important role. One important aspect is the connection between diffusion processes and linear partial differential equations of second order, which is in particular the basis for Monte Carlo numerical methods for linear PDEs. Since the pioneering work of Peng and Pardoux in the early 1990s, a new type of SDEs called backward stochastic differential equations (BSDEs) has emerged. The two main reasons why this new class of equations is important are the connection between BSDEs and semilinear PDEs, and the fact that BSDEs constitute a natural generalization of the famous Black and Scholes model from Mathematical Finance, and thus offer a natural mathematical framework for the formulation of many new models in Finance.Trade Review“This 668-page magnum opus of stochastic ODEs and PDEs belongs on the shelf of every researcher in these areas, as well as any mathematician or scientist who wants to learn more about the subject. … my opinion is that this book accomplished a Herculean task of making an arguably technical subject that is daunting to a beginner accessible. This book wants to be read!” (Mark A. McKibben, Mathematical Reviews, April, 2016)“The present monograph gives a rather complete treatment of backward stochastic differential equations as tool for the stochastic interpretation of second order PDEs. As the reader is guided from basic knowledge on stochastic analysis through the Itō calculus and the theory of stochastic differential equations to that of the backward equations, the monograph represents in my eyes a precious textbook for Master students, PhD students, but also specialists in this domain.” (Rainer Buckdahn, zbMATH 1321.60005, 2015)Table of ContentsIntroduction.- Background of Stochastic Analysis.- Ito’s Stochastic Calculus.- Stochastic Differential Equations.- SDE with Multivalued Drift.- Backward SDE.- Annexes.- Bibliography.- Index. ​ ​

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Book SynopsisThis is the revised and enlarged 2nd edition of the authors’ original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory. The present volume gives a substantial account of regression analysis, both for stochastic processes and measures, and includes recent material on Ridge regression with some unexpected applications, for example in econometrics.The first three chapters can be used for a quarter or semester graduate course on inference on stochastic processes. The remaining chapters provide more advanced material on stochastic analysis suitable for graduate seminars and discussions, leading to dissertation or research work. In general, the book will be of interest to researchers in probability theory, mathematical statistics and electrical and information theory.Trade Review“A wonderful text with a very high pedagogical and scientific quality, on inference theory in stochastic processes, important for researchers in probability theory, mathematical statistics and electrical and information theory.” (Prof. Dr. Manuel Alberto M. Ferreira, Acta Scientiae et Intellectus, Vol. 2 (1), 2016)“This book is the revised and enlarged edition of the author's original text … . The book is well written and will be of interest for researchers in probability theory and mathematical statistics.” (N. G. Gamkrelidze, zbMATH 1341.62036, 2016)Table of Contents1.Introduction and Preliminaries.- 2.Some Principles of Hypothesis Testing.- 3.Parameter Estimation and Asymptotics.- 4.Inferences for Classes of Processes.- 5.Likelihood Ratios for Processes.- 6.Sampling Methods for Processes.- 7.More on Stochastic Inference.- 8.Prediction and Filtering of Processes.- 9.Nonparametric Estimation for Processes.- Bibliography.- Index.

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Book SynopsisConsidering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integration theory, existence and uniqueness results and stability theory. The results will be of particular interest to natural scientists and the finance community. Readers should ideally be familiar with stochastic processes and probability theory in general, as well as functional analysis and in particular the theory of operator semigroups. ​Table of Contents1.Introduction.- 2.Preliminaries.- 3.Stochastic Integrals with Respect to Compensated Poisson Random Measures.- 4.Stochastic Integral Equations in Banach Spaces.- 5.Stochastic Partial Differential Equations in Hilbert Spaces.- 6.Applications.- 7.Stability Theory for Stochastic Semilinear Equations.- A Some Results on compensated Poisson random measures and stochastic integrals.- References.- Index.

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Book SynopsisThis highly anticipated second edition features new chapters and sections, 225 new references, and comprehensive R software. In keeping with the previous edition, this book is about the art and science of data analysis and predictive modelling, which entails choosing and using multiple tools. Instead of presenting isolated techniques, this text emphasises problem solving strategies that address the many issues arising when developing multi-variable models using real data and not standard textbook examples. Regression Modelling Strategies presents full-scale case studies of non-trivial data-sets instead of over-simplified illustrations of each method. These case studies use freely available R functions that make the multiple imputation, model building, validation and interpretation tasks described in the book relatively easy to do. Most of the methods in this text apply to all regression models, but special emphasis is given to multiple regression using generalised least squares for longitudinal data, the binary logistic model, models for ordinal responses, parametric survival regression models and the Cox semi parametric survival model. A new emphasis is given to the robust analysis of continuous dependent variables using ordinal regression.As in the first edition, this text is intended for Masters' or PhD. level graduate students who have had a general introductory probability and statistics course and who are well versed in ordinary multiple regression and intermediate algebra. The book will also serve as a reference for data analysts and statistical methodologists, as it contains an up-to-date survey and bibliography of modern statistical modelling techniques. Trade Review“The aim and scope of this edition to provide graduate students and professional and early career researchers with insights, understandings and working knowledge of regression modelling. … . The book is sequentially organized and well structured and many chapters are self-contained. It includes many useful topics and techniques for graduate .students and researchers alike. This book can be used as a textbook and equally as a reference book.” (Technometrics, Vol. 58 (2), February, 2016)Table of ContentsIntroduction.- General Aspects of Fitting Regression Models.- Missing Data.- Multivariable Modeling Strategies.- Describing, Resampling, Validating and Simplifying the Model.- R Software.- Modeling Longitudinal Responses using Generalized Least Squares.- Case Study in Data Reduction.- Overview of Maximum Likelihood Estimation.- Binary Logistic Regression.- Binary Logistic Regression Case Study 1.- Logistic Model Case Study 2: Survival of Titanic Passengers.- Ordinal Logistic Regression.- Case Study in Ordinal Regression, Data Reduction and Penalization.- Regression Models for Continuous Y and Case Study in Ordinal Regression.- Transform-Both-Sides Regression.- Introduction to Survival Analysis.- Parametric Survival Models.- Case Study in Parametric Survival Modeling and Model Approximation.- Cox Proportional Hazards Regression Model.- Case Study in Cox Regression.- Appendix.

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Book SynopsisThis second edition expands the first chapters, which focus on the approach to risk management issues discussed in the first edition, to offer readers a better understanding of the risk management process and the relevant quantitative phases. In the following chapters the book examines life insurance, non-life insurance and pension plans, presenting the technical and financial aspects of risk transfers and insurance without the use of complex mathematical tools. The book is written in a comprehensible style making it easily accessible to advanced undergraduate and graduate students in Economics, Business and Finance, as well as undergraduate students in Mathematics who intend starting on an actuarial qualification path. With the systematic inclusion of practical topics, professionals will find this text useful when working in insurance and pension related areas, where investments, risk analysis and financial reporting play a major role.Trade Review“This is a good introductory book on the topics. This book is clearly written for students in the arena of insurance industry. This is also a good reference book for professionals. … Each chapter of the book ends with a section providing bibliographic references and suggestions for further reading. … this is a good contribution, providing up-to-date coverage on selected insurance topics in a logical and systematic manner.” (Technometrics, Vol. 58 (2), February, 2016) Table of Contents1 Risks and Insurance.- 2 Managing a Portfolio of Risks.- Life Insurance: Modeling the Lifetime.- 4 Life Insurance: Pricing.- 5 Life Insurance: Reserving.- 6 Reserves and Profits in a Life Insurance Portfolio.- 7 Finance in Life Insurance: Linking Benefits to the Investment Performance.- 8 Pension Plans: Technical and Financial Perspectives.- 9 Non-life Insurance: Pricing and Reserving.- Index.

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Book SynopsisThis monograph provides a concise presentation of a mathematical approach to metastability, a wide-spread phenomenon in the dynamics of non-linear systems - physical, chemical, biological or economic - subject to the action of temporal random forces typically referred to as noise, based on potential theory of reversible Markov processes. The authors shed new light on the metastability phenomenon as a sequence of visits of the path of the process to different metastable sets, and focuses on the precise analysis of the respective hitting probabilities and hitting times of these sets.The theory is illustrated with many examples, ranging from finite-state Markov chains, finite-dimensional diffusions and stochastic partial differential equations, via mean-field dynamics with and without disorder, to stochastic spin-flip and particle-hop dynamics and probabilistic cellular automata, unveiling the common universal features of these systems with respect to their metastable behaviour. The monograph will serve both as comprehensive introduction and as reference for graduate students and researchers interested in metastability.Trade Review“This monograph gives a complete and detailed account of the most recent techniques developed to obtain a precise mathematical description of the phenomenon of metastability. … The book is well organized and well written, it contains a large amount of fundamental ideas and techniques, and it is an important reference for any researcher interested in the study of long-time behavior of Markov processes and applications to statistical mechanics.” (Jean-Baptiste Bardet, Mathematical Reviews, April, 2017)“No doubt, this is a fundamental book written by well established scientists whose contribution to this area is widely recognized. The book is addressed to readers with serious mathematical background and interests in metastability of stochastic dynamical systems. The books is also an excellent references source.” (Jordan M. Stoyanov, zbMATH 1339.60002, 2016)Table of ContentsPart I Introduction.- 1.Background and motivation.- 2.Aims and scopes.- Part II Markov processes 3.Some basic notions from probability theory.- 4.Markov processes in discrete time.- 5.Markov processes in continuous time.- 6.Large deviations.- 7.Potential theory.- Part III Metastability.- 8.Key definitions and basic properties.- 9.Basic techniques.- Part IV Applications: Diffusions with small noise.- 10.Discrete reversible diffusions.- 11.Diffusion processes with gradient drift.- 12.Stochastic partial differential equations.- Part V Applications: Coarse-graining at positive temperatures.- 13.The Curie-Weiss model.- 14.The Curie-Weiss model with a random magnetic field: discrete distributions.- 15.The Curie-Weiss model with random magnetic field: continuous distributions.- Part VI Applications: Lattice systems in small volumes at low temperatures.- 16.Abstract set-up and metastability in the zero-temperature limit.- 17.Glauber dynamics.- 18.Kawasaki dynamics.- Part VII Applications: Lattice systems in large volumes at low temperatures.- 19.Glauber dynamics.- 20.Kawasaki dynamics.- Part VIII Applications: Lattice systems in small volumes at high densities.- 21.The zero-range process.- Part IX Challenges.- 22.Challenges within metastability.- 23.Challenges beyond metastability.- References.-Glossary.- Index.

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Book SynopsisAus moderner Sicht werden in diesem Teubner-Taschenbuch die Grundlagen und wichtige Anwendungen der statistischen Physik dargestellt. Auf eine gründliche Darstellung der Begriffsbildungen der statistischen Physik, auf die korrekte Herleitung grundlegender Gleichungen und auf die Durchführung wichtiger Beweise wird besonderer Wert gelegt. Das Buch eignet sich als Begleittext für Kurs- und Spezialvorlesungen, als Repetitorium zur Prüfungsvorbereitung und als Nachschlagewerk zur raschen Information für breite Leserkreise aus Mathematik, Naturwissenschaften und technischen Disziplinen, insbesondere für Studenten dieser Fachrichtungen.Table of ContentsKombinatorik - Wahrscheinlichkeitstheorie - Quantenmechanik und Wahrscheinlichkeit - Thermodynamik - Statistische Physik der Gleichgewichtssysteme - Statistische Physik der Systeme im Nichtgleichgewicht - Statistische Physik und Informationstheorie - Phasenraummethoden der Quantenstatistik - Fraktaltheorie und Perkolationstheorie - Theorie dynamischer Systeme, Chaostheorie, Ergodentheorie - Statistische Thermodynamik chemischer Systeme - Statistische Theorie biologischer Systeme - Synergetik, weitere Anwendungen der statistischen Physik

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Book SynopsisReale Sachverhalte statistisch zu erschließen und zu analysieren ist eine hohe Kunst. Das Programmpaket SPSS ist dafür ein mächtiges Werkzeug. In diesem Buch lernen Sie anhand zahlreicher Beispiele, welche statistischen Verfahren es überhaupt gibt und wann welches Verfahren angemessen ist. Gleich im Anschluss erfahren Sie, wie diese Verfahren in SPSS implementiert sind und wie Sie sie in Ihrem Fachgebiet nutzen können. So finden Sie Zusammenhänge in Ihren Daten, die statistisch signifikant sind.Table of ContentsÜber den Autor 9 Einführung 23 Teil I: Grundlagen der statistischen Datenverarbeitung und von SPSS 29 Kapitel 1: Vorbemerkungen zu SPSS 31 Kapitel 2: Daten als Mütter statistischer Analysen 43 Kapitel 3: Hier wächst zusammen, was zusammengehört: Datendateien zusammenbringen 77 Kapitel 4: Datendateien in Form bringen 89 Kapitel 5: Was Sie an Syntax reinstecken, bekommen Sie an Output raus 135 Teil II Deskriptive SPSS-Statistiken 211 Kapitel 6: Von der Schönheit des Anhäufens: Eindimensionale Häufigkeitsverteilungen 213 Kapitel 7: Viele Wege führen nach Rom: Eindimensionale deskriptive Statistiken 233 Teil III Deskriptive und induktive SPSS-Statistiken gemischt 265 Kapitel 8: Was alles mehr oder weniger miteinander zusammenhängt: Mehrdimensionale Häufigkeitsverteilungen 267 Kapitel 9: Über Abhängigkeiten: Simple Regressionen 315 Kapitel 10: Komplexere Regressionen 387 Kapitel 11: Vom Gruppieren und Zusammenfassen von Daten: Diskriminanz- , Cluster- und Faktorenanalyse 397 Kapitel 12: Zeit spielt eine Rolle – und überhaupt: Überleben erwünscht! 433 Teil IV Induktive SPSS-Statistiken 455 Kapitel 13: Tests I: Welcher Mittelwert ist am größten? 457 Kapitel 14: Tests II: Glockenkurve – oder was? 491 Kapitel 15: Tests III: Was hängt mit wem zusammen? 507 Teil V SPSS-Syntax für Fortgeschrittene 515 Kapitel 16: Koppelung mit R und Python 517 Kapitel 17: Schleifen zum schnelleren Programmieren 527 Kapitel 18: Auch Makros machen das Leben leichter 541 Kapitel 19: Beispielhafte Syntaxprogramme 553 Teil VI Top-10-Teil 569 Kapitel 20: Die 10 wichtigsten SPSS-Befehle 571 Kapitel 21: Die 10 wichtigsten SPSS-Tipps 575 Abbildungsverzeichnis 579 Stichwortverzeichnis 599

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Book SynopsisDas Rahmenthema der 25. Jahrestagung der Deutschen Gesellschaft fur Medizinische DOkumentation, Informatik und Statistik e. V. - Nachsorge und Krankheitsverlaufsanalyse - hat einen engen Bezug zu aktuellen Problemen des Gesundheitswesens. Insbesondere in Kliniken, in denen schwere Erkrankungen mit modernen erfolgversprechenden Massnahmen be- handelt werden, wird die Notwendigkeit einer systematischen weiteren Uberwachung dieser Patienten immer dringlicher erachtet. Die Beob- achtung des weiteren Schicksals, die arztliche Betreuung und die Bewertung der zeitlichen Verlaufe ergeben Ansatzpunkte fur die weitere Verbesserung der Therapie. Diese Aufgabe lasst sich nur be- waltigen, wenn die dabei auftretenden Probleme der planvollen Doku- mentation, der Informationsubermittlung, der Datenspeicherung und der statistischen Auswertung von den Vertretern unseres Faches aktiv in Angriff genommen werden. Nach 25 Jahren einer sturmischen techno- logischen und Methodenentwicklung ist unsere junge medizinische Dis- ziplin in der Lage - wenn die erforderliche apparative und perso- nelle Ausstattung zur Verfugung steht -, die Probleme der Nachsorge und Krankheitsverlaufsanalyse in Zusammenarbeit mit Klinikern und Allgemeinmedizinern wirksam zu bearbeiten und Ergebnisse zu zeitigen, die fur den Arzt relevant sind. Die Tagung soll dazu Anregungen ver- mitteln und Losungswege aufzeigen. Funf Workshops und apparative, organisatorische und methodische Pro- bleme runden den Bezug unserer Arbeit auf die Probleme der !1edizin von heute ab. Erlangen hat eine traditionelle Verbundenheit mit der technologischen Entwicklung in der Medizin. Auch heute besteht, sowohl in der Medi- zinischen wie in der Technischen Fakultat, auf deren Campus wir tragen, ein waches Interesse fur den humanen Einsatz technologischer Neuerungen, insbesondere auch der elektronischen Datenverarbeitung. L.Table of ContentsErÖffnung der 25. Jahrestagung der Deutschen Gesellschaft FÜr Medizinische Dokumentation, Informatik und Statistik.- Zufall und lebendiges Geschehen.- Nachsorge und Krankheitsverlaufsanalyse-Einführung in die Thematik.- Nachsorge nach Krebsoperationen.- Probleme der Verlaufsbeobachtung und der prognostischen Beurteilung bei Herzkrankheiten.- Prognosestellung beim Rektumkarzinom mit Hilfe des COX-Modells.- Mathematische Modelle zur Analyse des Krankheitsverlaufs von Patienten mit Hirntumoren.- Analyse des Krankheitsverlaufs bei Prostatakarzinompatienten.- Statistische Auswertung des Krankheitsverlaufs von Tumorpatienten am Beispiel einer Studie über Karzinome der Mundhöhle.- Mehrkompartiment-Modelle in der Carcinogenese:Numerische Realisierung der Kleinste-Quadrate-Anpassung von Konzentrationsmessungen in der Maus.- Latenzzeitmessung bei Krebs am Beispiel einer Seite Fall-Kontroll-Studie an Lymphom- und Leukämiefällen in der amerikanischen Reifen- und Gummiindustrie.- Verlaufsuntersuchungen bei oralen Leukoplakien und Carcinomen.- Verteilungsfreie Teststatistiken bei Zen- sorierten Daten - Neue Entwicklungen.- Mathematisches Modell zur Prognose des Krankheitsverlaufs der Hepatitis B.- Methodische Probleme bei Langzeitstudien; insbesondere das Problem des Therapie-Abbruchs.- Nichtparametrischer Vergleich zweier Scharen von Verlaufskurven.- Anwendung eines Kompartimentmodelles zur Beurteilung von Behandlungsmethoden.- Probleme der statistischen Analyse einer Kohlenhydrat-Infusionsstudie.- Parametrische Tests für den Vergleich von Mittelwertsprofilen bei unverbundenen Beobachtungen mit homogenen Varianzen.- Variabilitätsuntersuchungen wesentlicher Spektralparameter im Verlaufe von EEG- Routine-Ableitungen.- Alternativen zur Bonferroni-Prozedur.- Variablenselektion bei multinomialen Klassifikationsproblemen.- Zur Problematik der Beurteilung abhängiger Häufigkeiten.- Explorative Datenanalyse - Schlußfolgerungen aus der Frühjahrstagung.- Die Integration der Nachsorgeorganisation und der Krankheitsverlaufsorganisation in ein allgemeines Befunddokumentationssystem.- Computerunterstützte Nachsorge und Krankheitsverlaufsanalyse – eine Komponente des medizinischen Auswertungssystems WAMAS.- Basisfunktionen für die Analyse von Verlaufsdaten.- ZEISIG Zytologisches Erfassungs- und Informationssystem in der Gynäkologie.- Betriebsärztliche Informationssysteme Schlußfolgerungen aus der Frühjahrstagung 1980.- Paket-Konzept und Refinement-Konstrukt Erste Erfahrungen mit einem Software-Entwicklungs-Instrument.- Verfahren zur Vereinheitlichung der Darstellung und Speicherung von Laborresultaten.- Implementierung eines Datenmodells auf einer operativen Intensivstation.- Das computergestützte Nachsorgesystem der I. Chirutgischen Universitätsklinik in Wien.- Computer-gestützte Nachsorge von Schrittmacher-Patienten.- Befunddokumentation in der hämostaseologischen Ambulanz der Medizinischen Hochschule Hannover.- Zur Frage des Aussagewertes einer routinemäßigen Thoraxübersichtsaufnahme bei der Diagnostik des Emphysems der Quarzstaublunge und dem Cor Pulmonale.- Auswertung von Krankheitsverläufen - Probleme und Lösungsmöglichkeiten: Dargestellt am Beispiel der akuten Virushepatitis.- Stoffwechselmetaboliten-Verlauf unter 48-stündiger Dauerinfusion von Glukose allein und in Mischung mit Sorbit, Fruktose oder Xylit bei Diabetikern.- EDV- Einsatz für die Bakteriologische Verlaufsund Befunddokumentation.- Erfassen und Auswerten von Antibiogrammen.- Institutionskarrieren schizophrener Kranker.- Das Fallregister psychisch Behinderter am PLK Weinsberg. Konzeption, Realisierung und erste Erfahrungen.- Prognose und Probleme der Verlaufsbeobachtung fokaler zerebraler Ischämie/Infarkte bei jungen Erwachsenen.- Langzeitverlauf nach Karotis-Operationen: Bedeutung der Neuropsychiatrischen Symptomatik.- Neuere Entwicklungen und Technologische Möglichkeiten der Mikroelektronik.- Ein Mikrorechner für die Eingliederung eines Analysenautomaten in dezentral organisierte Laborautomatisierungssysteme.- Mikroprozessoreinsatz im Physiologischen Labor.- Zur Bestimmung der Pulswellengeschwindigkeit.- On-line Verarbeitung von Hämoglobin-Reflexionsspektren hoher Repetitionsraten.- Anforderung an ein Mikroprozessorsystem zur Biosignalverarbeitung.- Entwurf und Aufbau eines Mikroprozessorsystems zur Biosignalverarbeitung.- Ein Mikrocomputer als Subsystem im 24-Stunden Betrieb.- Der Mikroprozessor als integrierender Bestandteil eines autonomen Meßplatzes im klinischen Laboratorium.- Implementierung des Programmes HES EKG in vor Ort auswertende Mikroprozessoren.- Erfahrungen im 3-jährigen Einsatz eines dezentralen Dokumentations- und Auskunftssystems für chronisch Kranke mit einem Minicomputer.- Ergebnisbericht der Moderatoren: Workshop 1 Mikroelektronik in der Medizin.- Die Basisdokumentation für Tumorkranke der Arbeitsgemeinschaft Deutscher Tumorzentren (ADT).- Das klinische Krebsregister des Tumorzentrums Köln.- Das Register für Onkologische Nachsorge der GBK in Münster.- Bericht über ein computergestütztes klinischpathologisches Krebsregister der ersten Ausbaustufe.- Ein klinisches Krebsregister als Basis für Nachsorge und statistische Auswertung – ein Erfahrungsbericht.- Das Dokumentations-, Kommunikations- und Organisations-System des Tumorzentrums Heidelberg/ Mannheim mit KRAZTUR.- Computerunterstützte Nachsorge und Basisdokumentation in der Radioonkologie.- Ein Patienteninformationssystem für die Strahlentherapie – Nachsorgeorganisation und Langzeitanalyse -.- Kooperative Dokumentation von Malignomen im Kindesalter.- Computerunterstütztes Magenbiopsieregister.- Computergestützte Erfassung und Nachsorge von Patienten mit kolorektalen Polypen.- Ergebnisbericht der Moderatoren: Workshop 2 Dokumentation, Datenverarbeitung und Statistik in medizinischen Krebszentren.- Therapiestudien im Kontext der Evaluationsforschung.- Organisatorische und methodische Probleme bei der Durchführung kontrollierter Psychopharmakastudien in der Praxis niedergelassener Ärzte.- Methodology and results of a long-term, controlled study of the effectiveness of immunosuppressive treatment of multiple sclerosis.- Der Wirksamkeitsnachweis in der Therapie des Ovarialkarzinoms.- Strategien zum Abbruch von kontrollierten Therapiestudien - Probleme und gegenwärtig diskutierte Ansätze.- Integrierung von Beobachtungen aus dem nichtärztlichen Bereich in die Krankheitsverlaufsanalysen.- Ergebnisbericht der Moderatoren: Workshop 3 Kontrollierte klinische Studien.- Klinische Datenverarbeitung in der Fakultät für Medizin der Technischen Universität München.- Klinische Basisdokumentation als Teil eines Informations-Systems in einem Rehabilitations-Krankenhaus Konzeption und Implementierung.- Klinische Dokumentation an einer Neurochirurgischen Klinik.- Dialogunterstützte klinische Dokumentation am Universitätsklinikum Göttingen.- Ergebnisbericht der Moderatoren: Workshop 4 Dokumentation und Verarbeitung klinischer Daten.- Verwaltung und Krankenhaus-Informationssystem Eine Strukturanalyse.- Untersuchung zur Inanspruchnahme eines Universitäts klinikums im stationären und ambulanten Bereich - durchgeführt an den Universitätskliniken Marburg.- Sind “Kurzlieger” einer Medizinischen Klinik für die Unterbringung in Hostelbetten geeignet? Die Bedeutung der Diagnosestatistik bei einer Planungsaufgabe.- Personalbedarfsplanung für den Krankenhaus-Pflegebereich mit Modellen der linearen Programmierung.- Lagerhaltung verderblicher medizinischer Güter.- Bedarfsgesteuerte Blutspenden mit TRAMIDIS.- Ergebnisbericht der Moderatoren: Workshop 5 Medizinökonomie.- Autorenverzeichnis.

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Book SynopsisProceedings of a Conference held in Heidelberg, September 10 - 14, 1984Table of ContentsStochastic spatial processes in biology: A concise historical survey.- Tests for space-time clustering.- Age distributions in birth and death processes.- Critical clustering in the two dimensional voter model.- Measure-valued processes Construction, qualitative behavior and stochastic geometry.- Dual processes in population genetics.- Some peculiar properties of a particle system with sexual reproduction.- Computer simulation of developmental processes in biology: Models for the developing limb.- Asymptotics and spatial growth of branching random fields.- Generation-dependent branching processes with immigration: convergence of distributions.- On a class of infinite particle systems evolving in a random environment.- Percolation processes and dimensionality.- Birth and death processes with killing and applications to parasitic infections.- Limit theorems for multitype branching random walks.- On the reproduction rate of the spatial general epidemic.- Nearest particle systems: Results and open problems.- Neutral models of geographical variation.- Stochastic measure diffusions as models of growth and spread.- L 2 convergence of certain random walks on Z d and related diffusions.- Random fields: Applications in cell biology.- Correlated percolation and repulsive particle systems.

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Book SynopsisThis second BiBoS volume surveys recent developments in the theory of stochastic processes. Particular attention is given to the interaction between mathematics and physics. Main topics include: statistical mechanics, stochastic mechanics, differential geometry, stochastic proesses, quantummechanics, quantum field theory, probability measures, central limit theorems, stochastic differential equations, Dirichlet forms.Table of ContentsJump processes related to the two dimensional dirac equation.- A constructive characterization of radon probability measures on infinite dimensional spaces.- A "Brownian motion" with constant speed.- The semi-martingale approach to the optimal resource allocation in the controlled labour-surplus economy.- A central limit theorem for the laplacian in regions with many small holes.- On dirichlet forms with random data—Recurrence and homogenization.- A nicolai map for supersymmetric quantum mechanics on riemannian manifolds.- Stochastic equations for some Euclidean fields.- Percolation of the two-dimensional ising model.- How do stochastic processes enter into physics?.- Estimates on the difference between succeeding eigenvalues and Lifshitz tails for random Schrödinger operators.- On identification for distributed parameter systems.- Fock space and probability theory.- On a transformation of symmetric markov process and recurrence property.- On absolute continuity of two symmetric diffusion processes.- Collective phenomena in stochastic particle systems.- Boundary problems for stochastic partial differential equations.- Generalized one-sided stable distributions.- Quantum fields, gravitation and thermodynamics.- Self-repellent random walks and polymer measures in two dimensions.- On the uniquness of the markovian self-adjoint extension.- Representations of the group of equivariant loops in SU(N).- Proof of an algebraic central limit theorem by moment generating functions.- Averaging and fluctuations of certain stochastic equations.- Semimartingale with smooth density — The problem of "nodes".

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Book SynopsisProof of the "Fundamental Theorem of Asset Pricing" in its general form by Delbaen and Schachermayer was a milestone in the history of modern mathematical finance and now forms the cornerstone of this book. Puts into book format a series of major results due mostly to the authors of this book. Embeds highest-level research results into a treatment amenable to graduate students, with introductory, explanatory background. Awaited in the quantitative finance community.Trade ReviewFrom the reviews: "As a learning device, I think this works really well. The second half of the book allows readers to ‘put to use’ the mathematics they learn in the first half. I really like the authors’ writing style. They provide plenty of intuitive insights and historical notes along the way as they formally develop concepts. … I recommend it highly to theoretically-inclined financial engineers and researchers." (www.riskbook.com, September, 2006) "The aim of the book, as the authors state … is to give the reader a guided tour through the mathematics of arbitrage. … The book will be of invaluable help to new researchers in the area of incomplete markets. A new graduate student wishing to do such research would start by reading the papers in the book. She or he now has a very good book to assist this study." (Angelos Dassios, Mathematical Reviews, Issue 2007 a)Table of ContentsA Guided Tour to Arbitrage Theory.- The Story in a Nutshell.- Models of Financial Markets on Finite Probability Spaces.- Utility Maximisation on Finite Probability Spaces.- Bachelier and Black-Scholes.- The Kreps-Yan Theorem.- The Dalang-Morton-Willinger Theorem.- A Primer in Stochastic Integration.- Arbitrage Theory in Continuous Time: an Overview.- The Original Papers.- A General Version of the Fundamental Theorem of Asset Pricing (1994).- A Simple Counter-Example to Several Problems in the Theory of Asset Pricing (1998).- The No-Arbitrage Property under a Change of Numéraire (1995).- The Existence of Absolutely Continuous Local Martingale Measures (1995).- The Banach Space of Workable Contingent Claims in Arbitrage Theory (1997).- The Fundamental Theorem of Asset Pricingfor Unbounded Stochastic Processes (1998).- A Compactness Principle for Bounded Sequences of Martingales with Applications (1999).

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Book SynopsisUnderstanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.Table of Contentsto the Theory of Linear Operators.- to Quantum Statistical Mechanics.- Elements of Operator Algebras and Modular Theory.- Quantum Dynamical Systems.- The Ideal Quantum Gas.- Topics in Spectral Theory.

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Book SynopsisData Science and Classification provides new methodological developments in data analysis and classification. The broad and comprehensive coverage includes the measurement of similarity and dissimilarity, methods for classification and clustering, network and graph analyses, analysis of symbolic data, and web mining. Beyond structural and theoretical results, the book offers application advice for a variety of problems, in medicine, microarray analysis, social network structures, and music.Trade ReviewFrom the reviews: "This book is a collection of papers presented at the Tenth Conference of the International Federation of Classification Societies. The contributors are primarily statisticians and computer scientists … . The typesetting and page layout are well done, and the graphics are very clear. … The main market for this book would be libraries, and researchers wanting a record of recent advances in statistical learning." (Jeffrey D. Picka, Technometrics, Vol. 49 (3), August, 2007)Table of ContentsSimilarity and Dissimilarity.- A Tree-Based Similarity for Evaluating Concept Proximities in an Ontology.- Improved Fréchet Distance for Time Series.- Comparison of Distance Indices Between Partitions.- Design of Dissimilarity Measures: A New Dissimilarity Between Species Distribution Areas.- Dissimilarities for Web Usage Mining.- Properties and Performance of Shape Similarity Measures.- Classification and Clustering.- Hierarchical Clustering for Boxplot Variables.- Evaluation of Allocation Rules Under Some Cost Constraints.- Crisp Partitions Induced by a Fuzzy Set.- Empirical Comparison of a Monothetic Divisive Clustering Method with the Ward and the k-means Clustering Methods.- Model Selection for the Binary Latent Class Model: A Monte Carlo Simulation.- Finding Meaningful and Stable Clusters Using Local Cluster Analysis.- Comparing Optimal Individual and Collective Assessment Procedures.- Network and Graph Analysis.- Some Open Problem Sets for Generalized Blockmodeling.- Spectral Clustering and Multidimensional Scaling: A Unified View.- Analyzing the Structure of U.S. Patents Network.- Identifying and Classifying Social Groups: A Machine Learning Approach.- Analysis of Symbolic Data.- Multidimensional Scaling of Histogram Dissimilarities.- Dependence and Interdependence Analysis for Interval-Valued Variables.- A New Wasserstein Based Distance for the Hierarchical Clustering of Histogram Symbolic Data.- Symbolic Clustering of Large Datasets.- A Dynamic Clustering Method for Mixed Feature-Type Symbolic Data.- General Data Analysis Methods.- Iterated Boosting for Outlier Detection.- Sub-species of Homopus Areolatus? Biplots and Small Class Inference with Analysis of Distance.- Revised Boxplot Based Discretization as the Kernel of Automatic Interpretation of Classes Using Numerical Variables.- Data and Web Mining.- Comparison of Two Methods for Detecting and Correcting Systematic Error in High-throughput Screening Data.- kNN Versus SVM in the Collaborative Filtering Framework.- Mining Association Rules in Folksonomies.- Empirical Analysis of Attribute-Aware Recommendation Algorithms with Variable Synthetic Data.- Patterns of Associations in Finite Sets of Items.- Analysis of Music Data.- Generalized N-gram Measures for Melodic Similarity.- Evaluating Different Approaches to Measuring the Similarity of Melodies.- Using MCMC as a Stochastic Optimization Procedure for Musical Time Series.- Local Models in Register Classification by Timbre.- Gene and Microarray Analysis.- Improving the Performance of Principal Components for Classification of Gene Expression Data Through Feature Selection.- A New Efficient Method for Assessing Missing Nucleotides in DNA Sequences in the Framework of a Generic Evolutionary Model.- New Efficient Algorithm for Modeling Partial and Complete Gene Transfer Scenarios.

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Book SynopsisThis volume contains detailed, worked-out notes of six main courses given at the Saint-Flour Summer Schools from 1985 to 1987.Table of ContentsLarge deviations and applications.- Applications of non-commutative fourier analysis to probability problems.- Random fields and diffusion processes.- Waves in one-dimensional random media.- Remarks on the point interaction approximation.- Geometric aspects of diffusions on manifolds.- Stochastic mechanics and random fields.

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Book SynopsisSince its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one- or more- dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean.Trade Review"The systematic character of the exposision, which makes from the widely ramified subject matter of the extensive literature a clear, masterly arranged whole, is a particularly valuable feature of this monograph." (Publicationes Mathematicae)Table of ContentsPrerequisites.- 1. The standard BRownian motion.- 1.1. The standard random walk.- 1.2. Passage times for the standard random walk.- 1.3. Hin?in’s proof of the de Moivre-laplace limit theorem.- 1.4. The standard Brownian motion.- 1.5. P. Lévy’s construction.- 1.6. Strict Markov character.- 1.7. Passage times for the standard Brownian motion.- Note l: Homogeneous differential processes with increasing paths.- 1.8. Kolmogorov’s test and the law of the iterated logarithm.- 1.9. P. Lévy’s Hölder condition.- 1.10. Approximating the Brownian motion by a random walk.- 2. Brownian local times.- 2.1. The reflecting Brownian motion.- 2.2. P. Lévy’s local time.- 2.3. Elastic Brownian motion.- 2.4. t+ and down-crossings.- 2.5. T+ as Hausdorff-Besicovitch 1/2-dimensional measure.- Note 1: Submartingales.- Note 2: Hausdorff measure and dimension.- 2.6. Kac’s formula for Brownian functionals.- 2.7. Bessel processes.- 2.8. Standard Brownian local time.- 2.9. BrowNian excursions.- 2.10. Application of the Bessel process to Brownian excursions.- 2.11. A time substitution.- 3. The general 1-dimensional diffusion.- 3.1. Definition.- 3.2. Markov times.- 3.3. Matching numbers.- 3.4. Singular points.- 3.5. Decomposing the general diffusion into simple pieces.- 3.6. Green operators and the space D.- 3.7. Generators.- 3.8. Generators continued.- 3.9. Stopped diffusion.- 4. Generators.- 4.1. A general view.- 4.2. G as local differential operator: conservative non-singular case.- 4.3. G as local differential operator: general non-singular case.- 4.4. A second proof.- 4.5. G at an isolated singular point.- 4.6. Solving G•u = ? u.- 4.7. G as global differential operator: non-singular case.- 4.8. G on the shunts.- 4.9. G as global differential operator: singular case.- 4.10. Passage times.- Note 1: Differential processes with increasing paths.- 4.11. Eigen-differential expansions for Green functions and transition densities.- 4.12. Kolmogorov’s test.- 5. Time changes and killing.- 5.1. Construction of sample paths: a general view.- 5.2. Time changes: Q = R1.- 5.3. Time changes: Q = [0, + ?).- 5.4. Local times.- 5.5. Subordination and chain rule.- 5.6. Killing times.- 5.7. Feller’s Brownian motions.- 5.8. Ikeda’s example.- 5.9. Time substitutions must come from local time integrals.- 5.10. Shunts.- 5.11. Shunts with killing.- 5.12. Creation of mass.- 5.13. A parabolic equation.- 5.14. Explosions.- 5.15. A non-linear parabolic equation.- 6. Local and inverse local times.- 6.1. Local and inverse local times.- 6.2. Lévy measures.- 6.3. t and the intervals of [0, + ?) - ?.- 6.4. A counter example: t and the intervals of [0, + ?) - ?.- 6.5a t and downcrossings.- 6.5b t as Hausdorff measure.- 6.5c t as diffusion.- 6.5d Excursions.- 6.6. Dimension numbers.- 6.7. Comparison tests.- Note 1: Dimension numbers and fractional dimensional capacities.- 6.8. An individual ergodic theorem.- 7. Brownian motion in several dimensions.- 7.1. Diffusion in several dimensions.- 7.2. The standard Brownian motion in several dimensions.- 7.3. Wandering out to ?.- 7.4. Greenian domains and Green functions.- 7.5. Excessive functions.- 7.6. Application to the spectrum of ?/2.- 7.7. Potentials and hitting probabilities.- 7.8. Newtonian capacities.- 7.9. Gauss’s quadratic form.- 7.10. Wiener’s test.- 7.11. Applications of Wiener’s test.- 7.12. Dirichlet problem.- 7.13. Neumann problem.- 7.14. Space-time Brownian motion.- 7.15. Spherical Brownian motion and skew products.- 7.16. Spinning.- 7.17. An individual ergodic theorem for the standard 2-dimensional BROWNian motion.- 7.18. Covering Brownian motions.- 7.19. Diffusions with Brownian hitting probabilities.- 7.20. Right-continuous paths.- 7.21. Riesz potentials.- 8. A general view of diffusion in several dimensions.- 8.1. Similar diffusions.- 8.2. G as differential operator.- 8.3. Time substitutions.- 8.4. Potentials.- 8.5. Boundaries.- 8.6. Elliptic operators.- 8.7. Feller’s little boundary and tail algebras.- List of notations.

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Book SynopsisThis book has been long awaited in the "interacting particle systems" community. Begun by Claude Kipnis before his untimely death, it was completed by Claudio Landim, his most brilliant student and collaborator. It presents the techniques used in the proof of the hydrodynamic behavior of interacting particle systems.Trade Review"Das Buch ist nach Meinung des Rezensenten eine gelungene Einführung in ein interessantes Gebiet der modernen Stochastik und mathematischen Physik und stellt einen fest umrissenen Gegenstand umfassend dar, vor allem den analytisch-methodischen Aspekt. ... Die Beweise sind übersichtlich und gut gegliedert, was das Nachvollziehen der Argumente sehr erleichtert; die didaktische Leistung der Autoren in diesem Punkt ist beeindruckend. Ein sorgfältig zusammengestelltes Literaturverzeichnis von etwa 400 Titeln schließt das Buch ab. Ingesamt ein sehr gut geschriebener und nützlicher Band."DMV Jahresbericht, 103. Band, Heft 3, November 2001Table of Contents1. An Introductory Example: Independent Random Walks.- 2. Some Interacting Particle Systems.- 3. Weak Formulations of Local Equilibrium.- 4. Hydrodynamic Equation of Symmetric Simple Exclusion Processes.- 5. An Example of Reversible Gradient System: Symmetric Zero Range Processes.- 6. The Relative Entropy Method.- 7. Hydrodynamic Limit of Reversible Nongradient Systems.- 8. Hydrodynamic Limit of Asymmetric Attractive Processes.- 9. Conservation of Local Equilibrium for Attractive Systems.- 10. Large Deviations from the Hydrodynamic Limit.- 11. Equilibrium Fluctuations of Reversible Dynamics.- Appendices.- 1. Markov Chains on a Countable Space.- 1.1 Discrete Time Markov Chains.- 1.2 Continuous Time Markov Chains.- 1.3 Kolmogorov’s Equations, Generators.- 1.4 Invariant Measures, Reversibility and Adjoint Processes.- 1.5 Some Martingales in the Context of Markov Processes.- 1.6 Estimates on the Variance of Additive Functionals of Markov Processes.- 1.7 The Feynman-Kac Formula.- 1.8 Relative Entropy.- 1.9 Entropy and Markov Processes.- 1.10 Dirichlet Form.- 1.11 A Maximal Inequality for Reversible Markov Processes.- 2. The Equivalence of Ensembles, Large Deviation Tools and Weak Solutions of Quasi-Linear Differential Equations.- 2.1 Local Central Limit Theorem and Equivalence of Ensembles.- 2.2 On the Local Central Limit Theorem.- 2.3 Remarks on Large Deviations.- 2.4 Weak Solutions of Nonlinear Parabolic Equations.- 2.5 Entropy Solutions of Quasi-Linear Hyperbolic Equations.- 3. Nongradient Tools: Spectral Gap and Closed Forms.- 3.1 On the Spectrum of Reversible Markov Processes.- 3.2 Spectral Gap for Generalized Exclusion Processes.- 3.4 Closed and Exact Forms.- 3.5 Comments and References.- References.

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Book SynopsisCe livre présente une catégorie de modèles probabilistes regroupés sous le nom de réseaux ou systèmes de files d'attente. Ces modèles interviennent dans de nombreuses applications, comme les réseaux de télecommunication ou les réseaux informatiques. Sur le plan théorique ils sont à la source d'une large classe de problèmes : marches aléatoires et diffusions réfléchies, processus ponctuels, etc. Ce livre présente les techniques probabilistes qui permettent d'étudier le comportement qualitatif de ces modèles.Table of ContentsProcessus ponctuels.- Le maximum d'une marche aléatoire.- Réversibilité et équations d'équilibre des réseaux.- La marche aléatoire simple réfléchie.- La file d'attente M/M/infini.- Les files d'attente avec une entrée poissonnienne.- Critères de stabilité.- Méthodes de renormalisation.- Théorie ergodique.- Processus ponctuels stationnaires.- La file d'attente G/G1 FIFO. Annexe.- Loi de Poisson et évènements rares.- Rappels sur les martingales.- Les processus markoviens de sauts.- Convergence en distribution.

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Book SynopsisAlthough three decades have passed since the first publication of this book, it is reprinted now as a result of popular demand. The content remains up-to-date and interesting for many researchers as is shown by the many references to it in current publications. The author is one of the leading experts of the field and gives an authoritative treatment of a subject.Table of ContentsRandom Processes: Markov Times.- Optimal Stopping of Markov Sequences.- Optimal Stopping of Markov Processes.- Some Applications to Problems of Mathematical Statistics.

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Book SynopsisThe 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. An entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.Trade ReviewFrom the reviews of the second edition:"The second edition (from 2008) contains a large additional chapter … entitled ‘Some Recent Developments’, where alternative attempts at a rigourous formalism are presented, as well as recent applications. Summarizing, this is a good and insightful book for those familiar with path integrals and curious about the mathematic foundations of path integration." (Jacques Tempere, Belgian Physical Society Magazine, Issue 2, June, 2009)“The new edition goes way beyond the habitual corrections and additions … . It is good to have this new book. Not only for the more recent results it contains, but also as a point of departure for so many questions that are still open in the realm of infinite dimensional oscillatory integrals.” (Ludwig Streit, Zentralblatt MATH, Vol. 1222, 2011)Table of ContentsThe Fresnel Integral of Functions on a Separable Real Hilbert Space.- The Feynman Path Integral in Potential Scattering.- The Fresnel Integral Relative to a Non-singular Quadratic Form.- Feynman Path Integrals for the Anharmonic Oscillator.- Expectations with Respect to the Ground State of the Harmonic Oscillator.- Expectations with Respect to the Gibbs State of the Harmonic Oscillator.- The Invariant Quasi-free States.- The Feynman History Integral for the Relativistic Quantum Boson Field.- Some Recent Developments.

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Book SynopsisAny method of fitting equations to data may be called regression. Such equations are valuable for at least two purposes: making predictions and judging the strength of relationships. Because they provide a way of em­ pirically identifying how a variable is affected by other variables, regression methods have become essential in a wide range of fields, including the soeial seiences, engineering, medical research and business. Of the various methods of performing regression, least squares is the most widely used. In fact, linear least squares regression is by far the most widely used of any statistical technique. Although nonlinear least squares is covered in an appendix, this book is mainly ab out linear least squares applied to fit a single equation (as opposed to a system of equations). The writing of this book started in 1982. Since then, various drafts have been used at the University of Toronto for teaching a semester-Iong course to juniors, seniors and graduate students in a number of fields, including statistics, pharmacology, pharmacology, engineering, economics, forestry and the behav­ ioral seiences. Parts of the book have also been used in a quarter-Iong course given to Master's and Ph.D. students in public administration, urban plan­ ning and engineering at the University of Illinois at Chicago (UIC). This experience and the comments and critieisms from students helped forge the final version.Table of Contents1 Introduction.- 2 Multiple Regression.- 3 Tests and Confidence Regions.- 4 Indicator Variables.- 5 The Normality Assumption.- 6 Unequal Variances.- 7 *Correlated Errors.- 8 Outliers and Influential Observations.- 9 Transformations.- 10 Multicollinearity.- 11 Variable Selection.- 12 *Biased Estimation.- A Matrices.- A.1 Addition and Multiplication.- A.2 The Transpose of a Matrix.- A.3 Null and Identity Matrices.- A.4 Vectors.- A.5 Rank of a Matrix.- A.6 Trace of a Matrix.- A.7 Partitioned Matrices.- A.8 Determinants.- A.9 Inverses.- A.10 Characteristic Roots and Vectors.- A.11 Idempotent Matrices.- A.12 The Generalized Inverse.- A.13 Quadratic Forms.- A.14 Vector Spaces.- Problems.- B Random Variables and Random Vectors.- B.1 Random Variables.- B.1.1 Independent Random Variables.- B.1.2 Correlated Random Variables.- B.1.3 Sample Statistics.- B.1.4 Linear Combinations of Random Variables.- B.2 Random Vectors.- B.3 The Multivariate Normal Distribution.- B.4 The Chi-Square Distributions.- B.5 The F and t Distributions.- B.6 Jacobian of Transformations.- B.7 Multiple Correlation.- Problems.- C Nonlinear Least Squares.- C.1 Gauss-Newton Type Algorithms.- C.1.1 The Gauss-Newton Procedure.- C.1.2 Step Halving.- C.1.3 Starting Values and Derivatives.- C.1.4 Marquardt Procedure.- C.2 Some Other Algorithms.- C.2.1 Steepest Descent Method.- C.2.2 Quasi-Newton Algorithms.- C.2.3 The Simplex Method.- C.2.4 Weighting.- C.3 Pitfalls.- C.4 Bias, Confidence Regions and Measures of Fit.- C.5 Examples.- Problems.- Tables.- References.- Author Index.

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Book SynopsisDas Arbeitsbuch führt in die Nutzung der Software Statistiklabor ein. Die Funktionalität wird im ersten Teil detailliert beschrieben, der zweite Teil illustriert Standardauswertungen. Die Software kann kostenfrei unter www.statistiklabor.de heruntergeladen werden. Sie bietet eine interaktive Arbeitsumgebung, um statistische Funktionen und Darstellungsmöglichkeiten leicht und intuitiv bearbeiten zu können, und erlaubt einen wesentlich einfacheren Zugang zu der umfangreichen Funktionalität der Statistik-Programmierumgebung R.Table of ContentsEine erste Beispielauswertung.- Die Oberfläche.- Ein- und Ausgabe.- Statistische Objekte.- Der Kalkulator.- Einiges zu R.- R-Grafik.- Spezielle Aspekte des Labors.- Beschreibung von Daten.- Wahrscheinlichkeitsrechnung.- Stichproben und Punktschätzungen.- Tests und Konfidenzintervalle.- Regression.- Tabellarische Überblicke.- Referenzen von R-Funktionen.- Liste typischer Auswertungen

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Book SynopsisIt was the end of 2005 when our employer, a major European Investment Bank, gave our team the mandate to compute in an accurate way the counterparty credit exposure arising from exotic derivatives traded by the ?rm. As often happens, - posure of products such as, for example, exotic interest-rate, or credit derivatives were modelled under conservative assumptions and credit of?cers were struggling to assess the real risk. We started with a few models written on spreadsheets, t- lored to very speci?c instruments, and soon it became clear that a more systematic approach was needed. So we wrote some tools that could be used for some classes of relatively simple products. A couple of years later we are now in the process of building a system that will be used to trade and hedge counterparty credit ex- sure in an accurate way, for all types of derivative products in all asset classes. We had to overcome problems ranging from modelling in a consistent manner different products booked in different systems and building the appropriate architecture that would allow the computation and pricing of credit exposure for all types of pr- ucts, to ?nding the appropriate management structure across Business, Risk, and IT divisions of the ?rm. In this book we describe some of our experience in modelling counterparty credit exposure, computing credit valuation adjustments, determining appropriate hedges, and building a reliable system.Table of ContentsMethodology.- Modelling Framework.- Simulation Models.- Valuation and Sensitivities.- Architecture and Implementation.- Computational Framework.- Implementation.- Architecture.- Products.- Interest-Rate Products.- Equity, Commodity, Inflation and FX Products.- Credit Derivatives.- Structures.- Hedging and Managing Counterparty Risk.- Counterparty Risk Aggregation and Risk Mitigation.- Combining Market and Credit Risk.- Pricing Counterparty Credit Risk.

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Book SynopsisThe present third edition of The Statistical Mechanics of Financial Markets is published only four years after the ?rst edition. The success of the book highlights the interest in a summary of the broad research activities on the application of statistical physics to ?nancial markets. I am very grateful to readers and reviewers for their positive reception and comments. Why then prepare a new edition instead of only reprinting and correcting the second edition? The new edition has been signi?cantly expanded, giving it a more pr- tical twist towards banking. The most important extensions are due to my practical experience as a risk manager in the German Savings Banks’ As- ciation (DSGV): Two new chapters on risk management and on the closely related topic of economic and regulatory capital for ?nancial institutions, - spectively, have been added. The chapter on risk management contains both the basics as well as advanced topics, e. g. coherent risk measures, which have not yet reached the statistical physics community interested in ?nancial m- kets. Similarly, it is surprising how little research by academic physicists has appeared on topics relating to Basel II. Basel II is the new capital adequacy framework which will set the standards in risk management in many co- tries for the years to come. Basel II is responsible for many job openings in banks for which physicists are extemely well quali?ed. For these reasons, an outline of Basel II takes a major part of the chapter on capital.Trade ReviewFrom the reviews of the third edition: "An excellent job of integrating many of the most important themes from econophysics in a relatively small volume. … The book serves its purpose, as a textbook on econophysics, superbly and one can tell that it developed from a course of lectures. The book is written with extreme clarity and an excellent pedagogical style. For philosophers who wish to acquaint themselves with the field of econophysics (beyond a superficial level), this is the book to invest in." (Dean Rickles, Studies in History and Philosophy of Modern Physics, Vol. 38, 2007)Table of ContentsIntroduction.- Basic Information on Capital Markets.- Random Walks in Finance and Physics.- The Black-Scholes Theory of Option Prices.- Scaling in Financial Data and in Physics.- Turbulence and Foreign Exchange Markets.- Derivative Pricing Beyond Black-Scholes.- Microscopic Market Models.- Theory of Stock Exchange Crashes.- Risk Management.- Economic and Regulatory Capital for Financial Institutions.- Appendix.- Notes and References.- Index.

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Book Synopsis"This is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion....This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises." –BULLETIN OF THE L.M.S.Trade ReviewThis is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion. The great strength of Revuz and Yor is the enormous variety of calculations carried out both in the main text and also (by implication) in the exercises. ... This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises, and throwing out challenging remarks about areas awaiting further research..." Bull.L.M.S. 24, 4 (1992) From the reviews of the third edition: "The authors have revised the second edition of their fundamental and impressive monograph on Brownian motion and continuous martingales … . The presentation of this book is unique in the sense that a concise and well-written text is complemented by a long series of detailed exercises. … This third edition contains some additional exercises related to recent advances in the subject. … is a valuable update of this basic reference book, which has been very helpful for researchers and students … ." (David Nualart, Zentralblatt MATH, Vol. 1087, 2006)Table of Contents0. Preliminaries.- I. Introduction.- II. Martingales.- III. Markov Processes.- IV. Stochastic Integration.- V. Representation of Martingales.- VI. Local Times.- VII. Generators and Time Reversal.- VIII. Girsanov’s Theorem and First Applications.- IX. Stochastic Differential Equations.- X. Additive Functionals of Brownian Motion.- XI. Bessel Processes and Ray-Knight Theorems.- XII. Excursions.- XIII. Limit Theorems in Distribution.- §1. Gronwall’s Lemma.- §2. Distributions.- §3. Convex Functions.- §4. Hausdorff Measures and Dimension.- §5. Ergodic Theory.- §6. Probabilities on Function Spaces.- §7. Bessel Functions.- §8. Sturm-Liouville Equation.- Index of Notation.- Index of Terms.- Catalogue.

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