Stochastics Books
Springer Nature Switzerland AG Advances in Probability and Mathematical
Book SynopsisThis volume contains papers which were presented at the XV Latin American Congress of Probability and Mathematical Statistics (CLAPEM) in December 2019 in Mérida-Yucatán, México. They represent well the wide set of topics on probability and statistics that was covered at this congress, and their high quality and variety illustrates the rich academic program of the conference.
£125.99
Springer Nature Switzerland AG Geometry and Invariance in Stochastic Dynamics:
Book SynopsisThis book grew out of the Random Transformations and Invariance in Stochastic Dynamics conference held in Verona from the 25th to the 28th of March 2019 in honour of Sergio Albeverio. It presents the new area of studies concerning invariance and symmetry properties of finite and infinite dimensional stochastic differential equations.This area constitutes a natural, much needed, extension of the theory of classical ordinary and partial differential equations, where the reduction theory based on symmetry and invariance of such classical equations has historically proved to be very important both for theoretical and numerical studies and has given rise to important applications.The purpose of the present book is to present the state of the art of the studies on stochastic systems from this point of view, present some of the underlying fundamental ideas and methods involved, and to outline the main lines for future developments. The main focus is on bridging the gap between deterministic and stochastic approaches, with the goal of contributing to the elaboration of a unified theory that will have a great impact both from the theoretical point of view and the point of view of applications. The reader is a mathematician or a theoretical physicist. The main discipline is stochastic analysis with profound ideas coming from Mathematical Physics and Lie’s Group Geometry. While the audience consists essentially of academicians, the reader can also be a practitioner with Ph.D., who is interested in efficient stochastic modelling.Table of ContentsAlbeverio, S., De Vecchi, F.C.: Some recent developments on Lie Symmetry analysis of stochastic differential equations.- Applebaum, D., Ming, L.: Markov processes with jumps on manifolds and Lie groups.- Cordoni, F., Di Persio, L.: Asymptotic expansion for a Black-Scholes model with small noise stochastic jump diffusion interest rate.- Cruzeiro, A.B., Zambrini, J.C.: Stochastic geodesics.- DeVecchi, F.C., Gubinelli, M.: A note on supersymmetry and stochastic differential equations.- Ebrahimi-Fard, K, Patras, F.: Quasi shuffle algebras in non-commutative stochastic calculus.- Elworthy, K.D.: Higher order derivatives of heat semigroups on spheres and Riemannian symmetric spaces.- Gehringer, J., Li, X.M.: Rough homogenisation with fractional dynamics.- Holm, D.D., Luesink, E.: Stochastic geometric mechanics with diffeomorphisms.- Izydorczyk, L., Oudjane, N., Russo, F.: McKean Feynman-Kac probabilistic representations of non linear partial differential equations.- Lescot, P., Valade, L.: Bernestein processes, isovectors and machanics.- Marinelli, C., Scarpa, L.: On the positivity of local mild solutions to stochastic evolution equations.- Privault, N.: Invariance of Poisson point processes by moment identities with statistical applications.
£123.49
Springer Nature Switzerland AG Perturbed Semi-Markov Type Processes I: Limit
Book SynopsisThis book is the first volume of a two-volume monograph devoted to the study of limit and ergodic theorems for regularly and singularly perturbed Markov chains, semi-Markov processes, and multi-alternating regenerative processes with semi-Markov modulation. The first volume presents necessary and sufficient conditions for weak convergence for first-rare-event times and convergence in the topology J for first-rare-event processes defined on regularly perturbed finite Markov chains and semi-Markov processes. The text introduces new asymptotic recurrent algorithms of phase space reduction. It also addresses both effective conditions of weak convergence for distributions of hitting times as well as convergence of expectations of hitting times for regularly and singularly perturbed finite Markov chains and semi-Markov processes. The book also contains a comprehensive bibliography of major works in the field. It provides an effective reference for both graduate students as well as theoretical and applied researchers studying stochastic processes and their applications. Trade Review“The book is concluded with the most up-to-date references, which complement these topics for the interested reader. This book is well-organized and expansive. … The results are properly motivated with precise, detailed proofs provided. This book is a must-have item for researchers interested in limit theorems as well as for other probability theorists.” (Steve Drekic, Mathematical Reviews, February, 2023)Table of ContentsPreface.- List of symbols.- Introduction.- Part I: First-Rare-Event Times for Regularly Perturbed Semi-Markov Processes.- Flows of Rare Events for Regularly Perturbed Semi-Markov Processes.- Generalizations of Limit Theorems for First-Rare-Event Times.- First-Rare-Event Times for Perturbed Risk Processes.- First-Rare-Event Times for Perturbed Closed Queuing Systems.- First-Rare-Event Times for Perturbed M/M-Type Queuing Systems.- Part II: Hitting Times and Phase Space Reduction for Perturbed Semi-Markov Processes.- Asymptotically Comparable Functions.- Perturbed Semi-Markov Processes and Reduction of Phase Space.- Asymptotics of Hitting Times for Perturbed Semi-Markov Processes.- Asymptotics for Expectations of Hitting Times for Perturbed Semi-Markov Processes.- Generalizations and Examples of Limit Theorems for Hitting Times.- Limit Theorems for Randomly Stopped Stochastic Processes.- Methodological and Bibliographical Notes.- References.- Index.
£98.99
Springer International Publishing AG Numerical Methods for Solving Discrete Event
Book SynopsisThis graduate textbook provides an alternative to discrete event simulation. It describes how to formulate discrete event systems, how to convert them into Markov chains, and how to calculate their transient and equilibrium probabilities. The most appropriate methods for finding these probabilities are described in some detail, and templates for efficient algorithms are provided. These algorithms can be executed on any laptop, even in cases where the Markov chain has hundreds of thousands of states. This book features the probabilistic interpretation of Gaussian elimination, a concept that unifies many of the topics covered, such as embedded Markov chains and matrix analytic methods.The material provided should aid practitioners significantly to solve their problems. This book also provides an interesting approach to teaching courses of stochastic processes. Trade Review“This monograph is an exciting addition to the queueing/stochastic processes literature, written by two highly respected senior researchers. … The writing is precise and clear. Well-known models are used as examples to illustrate the methods presented. … It has a huge number of powerful techniques that are not given sufficient focus elsewhere. This may be one of the best books to introduce graduate students … . This monograph is essential for the bookshelf … of every serious queueing theorist.” (Myron Hlynka, Mathematical Reviews, December, 2023)Table of ContentsBasic Concepts and Definitions.- Systems with Events Generated by Poisson or by Binomial Processes.- Generating the Transition Matrix.- Systems with Events Created by Renewal Processes.- Systems with Events Created by Phase-type Processes.- Computational Complexity and Rounding and Truncation Errors.- Transient Solutions of Markov Chains.- Moving Toward the Statistical Equilibrium.- Equilibrium Solutions of Markov Chains and Related Topics.- Reducing the State Space Through Censoring and Embedding.- Systems with Independent or Almost Independent Components.- Infinite-State Markov Chains and Matrix Analytic Methods.
£67.49
Springer International Publishing AG Measure Theory, Probability, and Stochastic
Book SynopsisThis textbook introduces readers to the fundamental notions of modern probability theory. The only prerequisite is a working knowledge in real analysis. Highlighting the connections between martingales and Markov chains on one hand, and Brownian motion and harmonic functions on the other, this book provides an introduction to the rich interplay between probability and other areas of analysis.Arranged into three parts, the book begins with a rigorous treatment of measure theory, with applications to probability in mind. The second part of the book focuses on the basic concepts of probability theory such as random variables, independence, conditional expectation, and the different types of convergence of random variables. In the third part, in which all chapters can be read independently, the reader will encounter three important classes of stochastic processes: discrete-time martingales, countable state-space Markov chains, and Brownian motion. Each chapter ends with a selection of illuminating exercises of varying difficulty. Some basic facts from functional analysis, in particular on Hilbert and Banach spaces, are included in the appendix. Measure Theory, Probability, and Stochastic Processes is an ideal text for readers seeking a thorough understanding of basic probability theory. Students interested in learning more about Brownian motion, and other continuous-time stochastic processes, may continue reading the author’s more advanced textbook in the same series (GTM 274).Table of ContentsPart I. Measure Theory.- Chapter 1. Measurable Spaces.- Chapter 2. Integration of Measurable Functions.- Chapter 3. Construction of Measures.- Chapter 4. Lp Spaces.- Chapter 5. Product Measure.- Chapter 6. Signed Measures.- Chapter 7. Change of Variables.- Part II. Probability Theory.- Chapter 8. Foundations of Probability Theory.- Chapter 9. Independence.- Chapter 10. Convergence of Random Variables.- Chapter 11. Conditioning.- Part III. Stochastic Processes.- Chapter 12. Theory of Martingales.- Chapter 13. Markov Chains.- Chapter 14. Brownian Motion.
£999.99
Springer International Publishing AG Stochastic Processes, Statistical Methods, and
Book SynopsisThe goal of the 2019 conference on Stochastic Processes and Algebraic Structures held in SPAS2019, Västerås, Sweden, from September 30th to October 2nd 2019, was to showcase the frontiers of research in several important areas of mathematics, mathematical statistics, and its applications. The conference was organized around the following topics1. Stochastic processes and modern statistical methods,2. Engineering mathematics,3. Algebraic structures and their applications.The conference brought together a select group of scientists, researchers, and practitioners from the industry who are actively contributing to the theory and applications of stochastic, and algebraic structures, methods, and models. The conference provided early stage researchers with the opportunity to learn from leaders in the field, to present their research, as well as to establish valuable research contacts in order to initiate collaborations in Sweden and abroad. New methods for pricing sophisticated financial derivatives, limit theorems for stochastic processes, advanced methods for statistical analysis of financial data, and modern computational methods in various areas of applied science can be found in this book. The principal reason for the growing interest in these questions comes from the fact that we are living in an extremely rapidly changing and challenging environment. This requires the quick introduction of new methods, coming from different areas of applied science. Advanced concepts in the book are illustrated in simple form with the help of tables and figures. Most of the papers are self-contained, and thus ideally suitable for self-study. Solutions to sophisticated problems located at the intersection of various theoretical and applied areas of the natural sciences are presented in these proceedings. Table of ContentsPart I. Stochastic Processes.- Chapter 1. Albuhayri, M., Engström, C., Malyarenko, A., Ni, Y., Silvestrov, S.: An improved asymptotics of implied volatility in the Gatheral model.- Chapter 2. Jamsher Ali, M., Pärna, K.: Ruin probability for merged risk processes with correlated arrivals.- Chapter 3. Nwe Aye, T., Carlsson, L.: Method Development for Emergent Properties in Stage-Structured Population Models with Stochastic Resource Growth.- Chapter 4. Golomoziy, V.: Computable bounds of exponential moments of simultaneous hitting time for two time-inhomogeneous atomic Markov chains.- Chapter 5. Jin, L., Dimitrov, M, Nim Y.: Valuation and Optimal Strategies for American Options under a Markovian Regime-Switching Model.- Chapter 6. Khusanbaev, Ya.M., Kudratov, Kh.E.: Inequalities for moments of branching processes in a varying environment.- Chapter 7. Kitouni, A., Messaci, F.: A law of the iterated logarithm for the empirical process based upon twice censored data.- Chapter 8. Kolias, P., Papadopoulou, A.: Investigating some attributes of periodicity in DNA sequences via semi-Markov modelling.- Chapter 9. Krasnitskiy, S., Kurchenko, S., Syniavska, O.: Limit Theorems of Baxter Type for Generalized Random Gaussian Processes with Independent Values.- Chapter 10. Lebedev, E., Ponomarov, V., Livinska, H.: On Explicit Formulas of Steady-State Probabilities for the M/M/c/c+m]-Type Retrial Queue.- Chapter 11. Malyarenko, A., Nohrouzian, H.: Testing Cubature Formulae on Wiener Space vs Explicit Pricing Formulae.- Chapter 12. Mishura, Y., Shevchenko, G., Shklyar, S.: Gaussian processes with Volterra kernels.- Chapter 13. Di Nunno, G., Mishura, Y., Ralchenko, K.: Stochastic differential equations driven by additive Volterra--Lévy and Volterra-Gaussian noises.- Chapter 14. Amechi Okeke, G., Abbas, M., Silvestrov, S.: Bochner integrability of the random fixed point of a generalized random operator and almost sure stability of some faster random iterative processes.- Chapter 15. Cruz Rambaud, S.: An Approach to the Absence of Price Bubbles through State-Price Deflators.- Chapter 16. da Silva, J.L., Drumond, C., Streit, L.: Form Factors for Stars Generalized Grey Brownian Motion.- Chapter 17. Silvestrov, D.: Flows of Rare Events for Regularly Perturbed Semi-Markov Processes. Part II. Statistical Methods.- Chapter 18. D’Amico, G., Di Basilio, B., Petroni, F., Gismondi, F.: An econometric analysis of drawdown based measures.- Chapter 19. Anisimov, V., Austin, M.: Forecasting and optimizing patient enrolment in clinical trials under various restrictions.- Chapter 20. Anguzu, C., Engström, C., Kasumba, H., Magero Mango, J.: Algorithms for Recalculating Alpha and Eigenvector Centrality Measures using Graph Partitioning Techniques.- Chapter 21. Kozachenko, Y., Rozora, I.: On statistical properties of the estimator of impulse response function.- Chapter 22. Keikara Muhumuza, A., Malyarenko, A., Silvestrov, S., Mango Magero, J., Kakuba, G.: Connections between the extreme points for Vandermonde determinants and minimizing risk measure in financial mathematics.- Chapter 23. Keikara Muhumuza, A., Malyarenko, A., Lundengard, K., Silvestrov, S., Mango Magero, J., Kakuba, G.: Extreme points of the Vandermonde Determinant and Wishart Ensemble on Symmetric Cones.- Chapter 24. Shchestyuk, N., Tyshenko, S.: Option Pricing and Stochastic Optimization.- Part III. Engineering Mathematics.- Chapter 25. Abela, M.S., Sunil Sharanappa, D.: MHD non-Darcy convective flow and heat transfer over a heated vertical plate embedded in a saturated porous medium in presence of viscous dissipation.- Chapter 26. Arjmand, D.: Numerical upscaling via the wave equation with perfectly matched layers.- Chapter 27. Canpwonyi, S., Carlsson, L.: On the Approximation of Physiologically Structured Population Model with a Three Stage-Structured Population Model in a Grazing System.- Chapter 28. Chandarki, I.M., Singh, B.B.: Homotopy Analysis Method (HAM) for Differential Equations pertaining to the Mixed Convection Boundary-Layer Flow over a Vertical Surface Embedded in a Porous Medium.- Chapter 29. Metri, P.G., Abel, M.S., Sunil Sharanappa, D.: Magnetohydrodynamic Casson nanofluid flow over a Nonlinear Stretching Sheet with Velocity Slip and Convective Boundary Conditions.- Chapter 30. Nankinga, L., Carlsson, L.: A Mathematical Model for Harvesting in a Stage-Structured Cannibalistic System.- Chapter 31. Tawade, J., Metri, P.G.: Mathematical and Computational Analysis of MHD Viscoelastic Fluid Flow and Heat Transfer over Stretching Surface Embedded in a Saturated Porous Medium.- Chapter 32. Tawade, J., Metri, P.G.: Numerical solution of boundary layer flow problem of a Maxwell fluid past a porous stretching surface.- Chapter 33. Umavathi, J.C., Metri, P.G., Silvestrov, S.: Effect of electromagnetic field on mixed convection of two immiscible conducting fluids in a vertical channel.- Chapter 34. Urekar, M.,Djordjević Kozarov, J.: Stochastic Smart Grid Meter for Industry 4.0 - From an Idea to the Practical Prototype.- Chapter 35. Vučković, A., Vučković, D., Perić, M., Raišević, N.: Magnetic force calculation between truncated cone shaped permanent magnet and soft magnetic cylinder using hybrid boundary element method.- Chapter 36. Vujičić, V., Djordjević Kozarov, J., Sovilj, P., Vujičić, B.: Mathematical basis of the stochastic digital measurement method.- Chapter 37. Ögren, M.: Stochastic solutions of Stefan problems.
£208.99
Springer International Publishing AG An Introduction to Anomalous Diffusion and Relaxation
Book SynopsisThis book provides a contemporary treatment of the problems related to anomalous diffusion and anomalous relaxation. It collects and promotes unprecedented applications dealing with diffusion problems and surface effects, adsorption-desorption phenomena, memory effects, reaction-diffusion equations, and relaxation in constrained structures of classical and quantum processes. The topics covered by the book are of current interest and comprehensive range, including concepts in diffusion and stochastic physics, random walks, and elements of fractional calculus. They are accompanied by a detailed exposition of the mathematical techniques intended to serve the reader as a tool to handle modern boundary value problems. This self-contained text can be used as a reference source for graduates and researchers working in applied mathematics, physics of complex systems and fluids, condensed matter physics, statistical physics, chemistry, chemical and electrical engineering, biology, and many others.Table of ContentsPreface.- Integral Transforms and Special Functions.- Concepts in Diffusion and Stochastic Processes.- Random Walks.- Elements of Fractional Calculus.- Fractional Anomalous Diffusion.- Adsorption Phenomena and Anomalous Behavior.- Reaction-Diffusion Problems.- Relaxation under Geometric Constraints I: Classical Processes.- Relaxation under Geometric Constraints II: Quantum Processes.- Index.
£49.49
Springer International Publishing AG An Introduction to Optimal Control Theory: The
Book SynopsisThis book introduces optimal control problems for large families of deterministic and stochastic systems with discrete or continuous time parameter. These families include most of the systems studied in many disciplines, including Economics, Engineering, Operations Research, and Management Science, among many others. The main objective is to give a concise, systematic, and reasonably self contained presentation of some key topics in optimal control theory. To this end, most of the analyses are based on the dynamic programming (DP) technique. This technique is applicable to almost all control problems that appear in theory and applications. They include, for instance, finite and infinite horizon control problems in which the underlying dynamic system follows either a deterministic or stochastic difference or differential equation. In the infinite horizon case, it also uses DP to study undiscounted problems, such as the ergodic or long-run average cost. After a general introduction to control problems, the book covers the topic dividing into four parts with different dynamical systems: control of discrete-time deterministic systems, discrete-time stochastic systems, ordinary differential equations, and finally a general continuous-time MCP with applications for stochastic differential equations. The first and second part should be accessible to undergraduate students with some knowledge of elementary calculus, linear algebra, and some concepts from probability theory (random variables, expectations, and so forth). Whereas the third and fourth part would be appropriate for advanced undergraduates or graduate students who have a working knowledge of mathematical analysis (derivatives, integrals, ...) and stochastic processes.Table of ContentsIntroduction: optimal control problems-. Discrete-time deterministic systems.- Discrete-time stochastic control systems.- Continuous-time deterministic systems.- Continuous-time Markov control processes.- Controlled diffusion processes.- Appendices.- Bibliography.- Index.
£49.49
Springer International Publishing AG Foundations of Modern Statistics: Festschrift in
Book SynopsisThis book contains contributions from the participants of the international conference “Foundations of Modern Statistics” which took place at Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, during November 6–8, 2019, and at Higher School of Economics (HSE University), Moscow, during November 30, 2019. The events were organized in honor of Professor Vladimir Spokoiny on the occasion of his 60th birthday. Vladimir Spokoiny has pioneered the field of adaptive statistical inference and contributed to a variety of its applications. His more than 30 years of research in the field of mathematical statistics had a great influence on the development of the mathematical theory of statistics to its present state. It has inspired many young researchers to start their research in this exciting field of mathematics. The papers contained in this book reflect the broad field of interests of Vladimir Spokoiny: optimal rates and non-asymptotic bounds in nonparametrics, Bayes approaches from a frequentist point of view, optimization, signal processing, and statistical theory motivated by models in applied fields. Materials prepared by famous scientists contain original scientific results, which makes the publication valuable for researchers working in these fields. The book concludes by a conversation of Vladimir Spokoiny with Markus Reiβ and Enno Mammen. This interview gives some background on the life of Vladimir Spokoiny and his many scientific interests and motivations. Table of ContentsOptimal rates and non-asymptotic bounds in nonparametrics: Z. Harchaoui, A. Juditsky, A. Nemirovski, D. Ostrovskii, Adaptive Denoising of Signals with Local Shift-Invariant Structure.- A. Dubois, Thomas B. Berret, C. Butucea, Goodness-of-fit testing for Hölder continuous densities under local differential privacy.- G. Blanchard and J.ean-Baptiste Fermanian, Nonasymptotic signal detection and two-sample tests in high dimension.- Sara van de Geer and P. Hinz, The Lasso with structured design and entropy of (absolute) convex hulls.- M. Hiabu, E. Mammen and Joseph-Theo Meyer, Local linear smoothing in additive models as data projection.- S. Ayvazyan and V. Ulyanov, A multivariate CLT for „typical“ weighted sums with rate of convergence of order O(1/n).- Estimation of matrices and subspaces: F. Götze, A. Tikhomirov, D. Timushev, Rate of convergence for sample covariance sparse matrices.- M. Wahl, Van Trees inequality, group equivariance, and estimation of principal subspaces.- D. Belomestny, E. Krymova, Sparse constrained projection approximation subspace tracking Nonparametric and semiparametric Bayes statistics.- Natalia Bochkina: Bernstein - von Mises theorem and misspecified models: a review.- M. Panov, On accuracy of Gaussian approximation in Bayesian semiparametric problems.- Statistical theory motivated by applications: M. Bl ́ehaut, X. D’Haultfœuille, J ́er ́emy L’Hour, A. B. Tsybakov, An alternative to synthetic control for models with many covariates under sparsity.- C. Breunig, X. Chen, Adaptive Estimation of Quadratic Functionals in Nonparametric Instrumental Variable Models.- G. Kulaitis, A. Munk and F. Werner, A minimax testing perspective on spatial statistical resolution in microscopy.- Optimisation: P. Dvurechensky, A. Gasnikov, A. Tyurin and V. Zholobov, Unifying Framework for Accelerated Randomized Methods in Convex Optimization.- K. Khowaja, M. Shcherbatyy and W. Karl Härdle. Surrogate Models for Optimization of Dynamical Systems.- Interview with Vladimir Spokoiny.
£142.49
Springer International Publishing AG Concentration and Gaussian Approximation for
Book SynopsisThis book describes extensions of Sudakov's classical result on the concentration of measure phenomenon for weighted sums of dependent random variables. The central topics of the book are weighted sums of random variables and the concentration of their distributions around Gaussian laws. The analysis takes place within the broader context of concentration of measure for functions on high-dimensional spheres. Starting from the usual concentration of Lipschitz functions around their limiting mean, the authors proceed to derive concentration around limiting affine or polynomial functions, aiming towards a theory of higher order concentration based on functional inequalities of log-Sobolev and Poincaré type. These results make it possible to derive concentration of higher order for weighted sums of classes of dependent variables.While the first part of the book discusses the basic notions and results from probability and analysis which are needed for the remainder of the book, the latter parts provide a thorough exposition of concentration, analysis on the sphere, higher order normal approximation and classes of weighted sums of dependent random variables with and without symmetries. Table of ContentsPart I. Generalities.- 1. Moments and correlation conditions.- 2. Some classes of probability distributions.- 3. Characteristic functions.- 4. Sums of independent random variables.- Part II. Selected topics on concentration.- 5. Standard analytic conditions.- 6. Poincaré-type inequalities.- 7. Logarithmic Sobolev inequalities.- 8. Supremum and infimum convolutions.- Part IV. Analysis on the sphere.- 9. Sobolev-type inequalities.- 10. Second order spherical concentration.- 11. Linear functionals on the sphere.- Part V. First applications to randomized sums.- 12. Typical distributions.- 13. Characteristic functions of weighted sums.- 14. Fluctuations of distributions.- Part VI. Refined bounds and rates.- 15. L^2 expansions and estimates.- 16. Refinements for the Kolmogorov distance.- 17. Applications of the second order correlation condition.- Part VII. Distributions and coefficients of special types.- 18. Special systems and examples.- 19. Distributions with symmetries.- 20. Product measures.- 21. Coefficients of Special type.- Glossary.
£113.99
Springer International Publishing AG Learning for Decision and Control in Stochastic
Book SynopsisThis book introduces the Learning-Augmented Network Optimization (LANO) paradigm, which interconnects network optimization with the emerging AI theory and algorithms and has been receiving a growing attention in network research. The authors present the topic based on a general stochastic network optimization model, and review several important theoretical tools that are widely adopted in network research, including convex optimization, the drift method, and mean-field analysis. The book then covers several popular learning-based methods, i.e., learning-augmented drift, multi-armed bandit and reinforcement learning, along with applications in networks where the techniques have been successfully applied. The authors also provide a discussion on potential future directions and challenges.Table of ContentsIntroduction.- The Stochastic Network Model.- Network Optimization Techniques.- Learning Network Decisions.- Summary and Discussions.
£42.74
Springer International Publishing AG Continuous Parameter Markov Processes and
Book SynopsisThis graduate text presents the elegant and profound theory of continuous parameter Markov processes and many of its applications. The authors focus on developing context and intuition before formalizing the theory of each topic, illustrated with examples.After a review of some background material, the reader is introduced to semigroup theory, including the Hille–Yosida Theorem, used to construct continuous parameter Markov processes. Illustrated with examples, it is a cornerstone of Feller’s seminal theory of the most general one-dimensional diffusions studied in a later chapter. This is followed by two chapters with probabilistic constructions of jump Markov processes, and processes with independent increments, or Lévy processes. The greater part of the book is devoted to Itô’s fascinating theory of stochastic differential equations, and to the study of asymptotic properties of diffusions in all dimensions, such as explosion, transience, recurrence, existence of steady states, and the speed of convergence to equilibrium. A broadly applicable functional central limit theorem for ergodic Markov processes is presented with important examples. Intimate connections between diffusions and linear second order elliptic and parabolic partial differential equations are laid out in two chapters, and are used for computational purposes. Among Special Topics chapters, two study anomalous diffusions: one on skew Brownian motion, and the other on an intriguing multi-phase homogenization of solute transport in porous media.Table of Contents1. A review of Martingaels, stopping times and the Markov property.- 2. Semigroup theory and Markov processes.-3. Regularity of Markov process sample paths.- 4. Continuous parameter jump Markov processes.- 5. Processes with independent increments.- 6. The stochastic integral.- 7. Construction of difficusions as solutions of stochastic differential equations.- 8. Itô's Lemma.- 9. Cameron-Martin-Girsanov theorem.- 10. Support of nonsingular diffusions.- 11. Transience and recurrence of multidimensional diffusions.- 12. Criteria for explosion.- 13. Absorption, reflection and other transformations of Markov processes.- 14. The speed of convergence to equilibrium of discrete parameter Markov processes and Diffusions.- 15. Probabilistic representation of solutions to certain PDEs.- 16. Probabilistic solution of the classical Dirichlet problem.- 17. The functional Central Limit Theorem for ergodic Markov processes.- 18. Asymptotic stability for singular diffusions.- 19. Stochastic integrals with L2-Martingales.- 20. Local time for Brownian motion.- 21. Construction of one dimensional diffusions by Semigroups.- 22. Eigenfunction expansions of transition probabilities for one-dimensional diffusions.- 23. Special Topic: The Martingale Problem.- 24. Special topic: multiphase homogenization for transport in periodic media.- 25. Special topic: skew random walk and skew Brownian motion.- 26. Special topic: piecewise deterministic Markov processes in population biology.- A. The Hille-Yosida theorem and closed graph theorem.- References.- Related textbooks and monographs.
£79.99
Birkhauser Verlag AG Discrete-Time Semi-Markov Random Evolutions and
Book SynopsisThis book extends the theory and applications of random evolutions to semi-Markov random media in discrete time, essentially focusing on semi-Markov chains as switching or driving processes. After giving the definitions of discrete-time semi-Markov chains and random evolutions, it presents the asymptotic theory in a functional setting, including weak convergence results in the series scheme, and their extensions in some additional directions, including reduced random media, controlled processes, and optimal stopping. Finally, applications of discrete-time semi-Markov random evolutions in epidemiology and financial mathematics are discussed. This book will be of interest to researchers and graduate students in applied mathematics and statistics, and other disciplines, including engineering, epidemiology, finance and economics, who are concerned with stochastic models of systems.Table of Contents- 1. Discrete-Time Stochastic Calculus in Banach Space. - 2. Discrete-Time Semi-Markov Chains. - 3. Discrete-Time Semi-Markov Random Evolutions. - 4. Weak Convergence of DTSMRE in Series Scheme. - 5. DTSMRE in Reduced Random Media. - 6. Controlled Discrete-Time Semi-Markov Random Evolutions. - 7. Epidemic Models in Random Media. - 8. Optimal Stopping of Geometric Markov Renewal Chains and Pricing.
£98.99
Springer International Publishing AG Probability: An Introduction Through Theory and
Book SynopsisThis textbook offers a complete one-semester course in probability, covering the essential topics necessary for further study in the areas of probability and statistics. The book begins with a review of the fundamentals of measure theory and integration. Probability measures, random variables, and their laws are introduced next, along with the main analytic tools for their investigation, accompanied by some applications to statistics. Questions of convergence lead to classical results such as the law of large numbers and the central limit theorem with their applications also to statistical analysis and more. Conditioning is the next main topic, followed by a thorough introduction to discrete time martingales. Some attention is given to computer simulation. Through the text, over 150 exercises with full solutions not only reinforce the concepts presented, but also provide students with opportunities to develop their problem-solving skills, and make this textbook suitable for guided self-study. Based on years of teaching experience, the author's expertise will be evident in the clear presentation of material and the carefully chosen exercises. Assuming familiarity with measure and integration theory as well as elementary notions of probability, the book is specifically designed for teaching in parallel with a first course in measure theory. An invaluable resource for both instructors and students alike, it offers ideal preparation for further courses in statistics or probability, such as stochastic calculus, as covered in the author's book on the topic.Table of Contents1 Elements of Measure Theory.- 2 Probability.- 3 Convergence.- 4 Conditioning.- 5 Martingales.- 6 Complements.- 7 Solutions.
£999.99
Springer International Publishing AG Potential Functions of Random Walks in ℤ with
Book SynopsisThis book studies the potential functions of one-dimensional recurrent random walks on the lattice of integers with step distribution of infinite variance. The central focus is on obtaining reasonably nice estimates of the potential function. These estimates are then applied to various situations, yielding precise asymptotic results on, among other things, hitting probabilities of finite sets, overshoot distributions, Green functions on long finite intervals and the half-line, and absorption probabilities of two-sided exit problems.The potential function of a random walk is a central object in fluctuation theory. If the variance of the step distribution is finite, the potential function has a simple asymptotic form, which enables the theory of recurrent random walks to be described in a unified way with rather explicit formulae. On the other hand, if the variance is infinite, the potential function behaves in a wide range of ways depending on the step distribution, which the asymptotic behaviour of many functionals of the random walk closely reflects.In the case when the step distribution is attracted to a strictly stable law, aspects of the random walk have been intensively studied and remarkable results have been established by many authors. However, these results generally do not involve the potential function, and important questions still need to be answered. In the case where the random walk is relatively stable, or if one tail of the step distribution is negligible in comparison to the other on average, there has been much less work. Some of these unsettled problems have scarcely been addressed in the last half-century. As revealed in this treatise, the potential function often turns out to play a significant role in their resolution. Aimed at advanced graduate students specialising in probability theory, this book will also be of interest to researchers and engineers working with random walks and stochastic systems. Table of ContentsPreface.- Introduction.- Preliminaries.- Bounds of the Potential Function.- Some Explicit Asymptotic Forms of a(x).- Applications Under m+/m → 0.- The Two-Sided Exit Problem – General Case.- The Two-Sided Exit Problem for Relatively Stable Walks.- Absorption Problems for Asymptotically Stable Random Walks.- Asymptotically Stable RandomWalks Killed Upon Hitting a Finite Set.- Appendix.- References.- Notation Index.- Subject Index.
£49.49
Springer International Publishing AG Practical Applications of Stochastic Modelling:
Book SynopsisThis book constitutes the referred proceedings of the 11th International Workshop on Practical Applications of Stochastic Modelling, PASM 2022, was held in Alicante, Spain, in September 2022.The 7 full papers presented in this volume were carefully reviewed and selected from 9 submissions. The papers demonstrate a diverse set of applications and approaches of stochastic modelling.Table of ContentsPerformance modelling of attack graphs.- Towards Calculating the Resilience of a Urban Transport Network under Attack.- Analysis of the Battery Level in Complex Wireless Sensor Networks using a Two Time Scales Second Order Fluid Model.- To Confine or not to Confine: A Mean Field Game Analysis of the End of an Epidemic.- Data Center Organization and Optimization Strategy as a k-ary n-cube Topology.- Towards energy-aware management of shared printers.- Modelling Performance and Fairness of Frame Bursting in IEEE 802.11n using PEPA.
£49.49
Springer International Publishing AG Marginal and Functional Quantization of
Book SynopsisVector Quantization, a pioneering discretization method based on nearest neighbor search, emerged in the 1950s primarily in signal processing, electrical engineering, and information theory. Later in the 1960s, it evolved into an automatic classification technique for generating prototypes of extensive datasets. In modern terms, it can be recognized as a seminal contribution to unsupervised learning through the k-means clustering algorithm in data science. In contrast, Functional Quantization, a more recent area of study dating back to the early 2000s, focuses on the quantization of continuous-time stochastic processes viewed as random vectors in Banach function spaces. This book distinguishes itself by delving into the quantization of random vectors with values in a Banach space—a unique feature of its content. Its main objectives are twofold: first, to offer a comprehensive and cohesive overview of the latest developments as well as several new results in optimal quantization theory, spanning both finite and infinite dimensions, building upon the advancements detailed in Graf and Luschgy's Lecture Notes volume. Secondly, it serves to demonstrate how optimal quantization can be employed as a space discretization method within probability theory and numerical probability, particularly in fields like quantitative finance. The main applications to numerical probability are the controlled approximation of regular and conditional expectations by quantization-based cubature formulas, with applications to time-space discretization of Markov processes, typically Brownian diffusions, by quantization trees. While primarily catering to mathematicians specializing in probability theory and numerical probability, this monograph also holds relevance for data scientists, electrical engineers involved in data transmission, and professionals in economics and logistics who are intrigued by optimal allocation problems.Table of ContentsPreface.- Notation Index.- Part I. Basics and Marginal Quantization.- 1. Optimal and Stationary Quantizers.- 2. The Finite-Dimensional Setting I.- 3. The Finite-Dimensional Setting II.- Part II. Functional Quantization.- 4. Functional Quantization, Small Ball Probabilities, Metric Entropy and Series Expansions for Gaussian Processes.- 5. Spectral Methods for Gaussian Processes.- 6. Geometry of Optimal and Rate-Optimal Quantizers for Gaussian Processes.- 7. Mean Regular Processes.- Part III. Algorithmic Aspects and Applications:- 8. Optimal Quantization from the Numerical Side (Static).- 9. Applications: Quantization-Based Cubature Formulas.- 10. Quantization-Based Numerical Schemes.- Appendices.- A. Radon Random Vectors, Stochastic Processes and Inequalities.- B. Miscellany.- References.- Index.
£161.99
Springer International Publishing AG Proceedings of the 6th International Symposium on
Book SynopsisThis proceedings book covers a wide range of topics related to uncertainty analysis and its application in various fields of engineering and science. It explores uncertainties in numerical simulations for soil liquefaction potential, the toughness properties of construction materials, experimental tests on cyclic liquefaction potential, and the estimation of geotechnical engineering properties for aerogenerator foundation design. Additionally, the book delves into uncertainties in concrete compressive strength, bio-inspired shape optimization using isogeometric analysis, stochastic damping in rotordynamics, and the hygro-thermal properties of raw earth building materials. It also addresses dynamic analysis with uncertainties in structural parameters, reliability-based design optimization of steel frames, and calibration methods for models with dependent parameters. The book further explores mechanical property characterization in 3D printing, stochastic analysis in computational simulations, probability distribution in branching processes, data assimilation in ocean circulation modeling, uncertainty quantification in climate prediction, and applications of uncertainty quantification in decision problems and disaster management. This comprehensive collection provides insights into the challenges and solutions related to uncertainty in various scientific and engineering contexts.Table of ContentsUncertainties of numerical simulation for static liquefaction potential of saturated soils.- Uncertainties about the Toughness Property of raw earth construction materials.- Uncertainties of Experimental Tests on Cyclic Liquefaction Potential of Unsaturated Soils.- Analysis of the Impact of Uncertainties on the Estimation of Geotechnical Engineering Properties of Soil from SPT on the Design of Aerogenerators Foundation.- Uncertainties on the unconfined compressive strength of raw and textured concrete.- Bio-inspired shape optimization for structural robust design using isogeometric analysis.
£189.99
Springer Hidden Markov Processes and Adaptive Filtering
Book Synopsis1 Auxiliary Result.- 2 Small Noise in Both Equations.- 3 Small Noise in Observations.- 4 Hidden Ergodic O-U process.- 5 Hidden Telegraph Process.- 6 Hidden AR Process.- 7 Source Localization.
£151.99
De Gruyter Stochastic Calculus of Variations: For Jump
Book SynopsisThis book is a concise introduction to the stochastic calculus of variations for processes with jumps. The author provides many results on this topic in a self-contained way for e.g., stochastic differential equations (SDEs) with jumps. The book also contains some applications of the stochastic calculus for processes with jumps to the control theory, mathematical finance and so. This third and entirely revised edition of the work is updated to reflect the latest developments in the theory and some applications with graphics.
£147.72
Birkhauser Verlag AG Introduction to Probability with Statistical
Book SynopsisNow in its second edition, this textbook serves as an introduction to probability and statistics for non-mathematics majors who do not need the exhaustive detail and mathematical depth provided in more comprehensive treatments of the subject. The presentation covers the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal distributions. More classical examples such as Montmort's problem, the ballot problem, and Bertrand’s paradox are now included, along with applications such as the Maxwell-Boltzmann and Bose-Einstein distributions in physics.Key features in new edition:* 35 new exercises* Expanded section on the algebra of sets * Expanded chapters on probabilities to include more classical examples* New section on regression* Online instructors' manual containing solutions to all exercises<Advanced undergraduate and graduate students in computer science, engineering, and other natural and social sciences with only a basic background in calculus will benefit from this introductory text balancing theory with applications.Review of the first edition: This textbook is a classical and well-written introduction to probability theory and statistics. … the book is written ‘for an audience such as computer science students, whose mathematical background is not very strong and who do not need the detail and mathematical depth of similar books written for mathematics or statistics majors.’ … Each new concept is clearly explained and is followed by many detailed examples. … numerous examples of calculations are given and proofs are well-detailed." (Sophie Lemaire, Mathematical Reviews, Issue 2008 m)Trade Review“Schay (emer., Univ. of Massachusetts) has created a text for a two semester, calculus-based course in mathematical statistics. … The prose reads well. Physical production is good. … Summing Up: Recommended. Upper-division undergraduates and graduate students.” (W. R. Lee, Choice, Vol. 54 (6), February, 2017)“I believe that students concentrating in mathematics and related subjects will find this book readable and interesting. … I think that students learning the probability for the first time will get real value out of working through the examples and exercises of the text. … Introduction to Probability with Statistical Applications is very clearly written and reading the book is enjoyable. I would certainly recommend Schay’s book as a primary textbook for an undergraduate course in calculus-based probability.” (Jason M. Graham, MAA Reviews, September, 2016)Table of ContentsIntroduction.- The Algebra of Events.- Combinatorial Problems.- Probabilities.- Random Variables.- Expectation, Variance, Moments.- Some Special Distributions.- The Elements of Mathematical Statistics.
£61.74
Springer International Publishing AG Œuvres Complètes—Collected Works
Book SynopsisThis book contains all of Wolfgang Doeblin's publications. In addition, it includes a reproduction of the pli cacheté on l'équation de Kolmogoroff and previously unpublished material that Doeblin wrote in 1940. The articles are accompanied by commentaries written by specialists in Doeblin's various areas of interest. The modern theory of probability developed between the two World Wars thanks to the very remarkable work of Kolmogorov, Khinchin, S.N. Bernstein, Romanovsky, von Mises, Hostinsky, Onicescu, Fréchet, Lévy and others, among whom one name shines particularly brightly, that of Wolfgang Doeblin (1915–1940). The work of this young mathematician, whose life was tragically cut short by the war, remains even now, and indeed will remain into the future, an exemplar of originality and of mathematical power. This book was conceived and in essence brought to fruition by Marc Yor before his death in 2014. It is dedicated to him.Trade Review“It attracted interest not only by mathematicians or some probability theory specialists, but also by the public, which normally would not be that interested in mathematics. … the editors gathered not only all published articles of W. Doeblin, but also some more papers, especially the ‘cahier jaune’ (yellow notebook). In comments and annotations the contents of the papers are put into today’s context by probability theory specialists. The book is excellent, a large and substantial work.” (Silke Göbel, zbMATH 1460.01019, 2021)Table of ContentsJ.-M. Bismut, Avant-propos.- H. Föllmer, Geleitwort.- B. Bru, Preface.- Part I The Life of Wolfgang Doeblin March 17, 1915 – June 21, 1940: B. Bru, Biographical Summary.- W. Doeblin, Autobiographical Note.- W. Doeblin (with remarks by B. Bru and E. Seneta), Notice sur les travaux.- List of Works of Wolfgang Doeblin.- Conversion Table.- T. Lindvall, W. Doeblin 1915–1940.- B. Bru and M. Yor, La vie de Doeblin et le pli cacheté 11.668.- B. Bru and M. Yor, Comments on the Life and Mathematical Legacy of Wolfgang Doeblin.-B. Bru and E. Seneta, Two Letters of W. Doeblin to A. N. Kolmogorov.- Part II Markov Chains: E. Seneta, Doeblin on Discrete Markov Chains.- M. Iosifescu, On Doeblin and Fortet’s paper “Sur des chaînes à liaisons complètes”.- M. Iosifescu, On Doeblin’s paper “Remarques sur la théorie métrique des fractions continues”.- E. Nummelin, Doeblin’s Theory of Markov Chains on a General Measurable State Space.- W. Doeblin, Sur les chaînes discrètes de Markoff [1936b].- W. Doeblin, Errata 1: Sur les chaînes discrètes de Markoff [1936c].- W. Doeblin, Errata 2: Sur les chaînes discrètes de Markoff [1936d].- W. Doeblin, Sur les chaînes de Markoff [1936e].- W. Doeblin and R. Fortet, Sur deux notes de MM. Kryloff et Bogoliouboff [1937e].- W. Doeblin, Éléments d’une théorie générale des chaînes constantes simples de Markoff [1937f].- W. Doeblin, Le cas discontinu des probabilités en chaîne [1937a].- W. Doeblin, Sur le cas continu des probabilités en chaîne [1937b].- W. Doeblin, and Robert Fortet Sur des chaînes à liaisons complètes [1937c].- W. Doeblin, Sur l’équation de Smoluchowsky [1937d].- W. Doeblin, Sur les propriétés asymptotiques de mouvements régis par certains types de chaînes simples [1938g] (reprint of [1937g] and [1937h]).- W. Doeblin, Sur l’équation matricielle A(t+s) = [A(t)A(s)] et ses applications aux probabilités en chaîne [1938a].-W. Doeblin, Sur l’équation matricielle A(t+s) = [A(t)A(s)] et ses applications au calcul des probabilités [1940a].- W. Doeblin, Sur deux problèmes de M. Kolmogoroff concernant les chaînes dénombrables [1938f].- W. Doeblin, Exposé de la théorie des chaînes simples constantes de Markoff à un nombre fini d’états [1938e].- W. Doeblin, Remarques sur la théorie métrique des fractions continues [1940d.- W. Doeblin, Éléments d’une théorie générale des chaînes simples constantes de Markoff [1940e].- Part III Sums of Independent Random Variables: D. M. Mason, Notes on Wolfgang Doeblin’s 1940 paper: L’ensemble de puissances d’une loi de probabilité.- W. Doeblin and P. Lévy, Sur les sommes de variables aléatoires indépendantes à dispersions bornées inférieurement [1936a].- W. Doeblin, Premiers éléments d’une étude systématique de l’ensemble de puissances d’une loi de probabilité [1938b].- W. Doeblin, Étude de l’ensemble de puissances d’une loi de probabilité [1938c].- W. Doeblin, Sur les sommes d’un grand nombre de vecteurs aléatoires [1938d].- W. Doeblin, Sur un problème de calcul des probabilités [1939b].- W. Doeblin, Sur les sommes d’un grand nombre de variables aléatoires indépendantes [1939c].- W. Doeblin, Sur l’ensemble de puissances d’une loi de probabilité (1940) [1940f].- W. Doeblin (with remarks by B. Bru and E. Seneta), Sur l’ensemble de puissances d’une loi de probabilité [1946].- Part IV Chapman’s Equations. Part IV.1 Documents Published Before the pli cacheté: W. Doeblin (with a remark by B. Bru), Sur certaines mouvements aléatoires discontinus [1939d].- W. Doeblin, Sur l’équation de Kolmogoroff [1938h].- W. Doeblin, Sur certains mouvements aléatoires [1939a].- W. Doeblin, Sur l’équation de Kolmogoroff [1940b].- W. Doeblin, Sur des mouvements mixtes [1940c].- Part IV.2 The pli cacheté: M. Yor, Présentation du pli cacheté.- W. Doeblin (with remarks by Bernard Bru and Marc Yor), Sur l’équation de Kolmogoroff, pli cacheté déposé le 26 février 1940, ouvert le 18 mai 2000 [1940g/2000].- B. Bru, Notes de lecture du pli cacheté.- W. Doeblin (with remarks by Bernard Bru), Exposé(s) sur l’équation de Chapman [1938i/2000].- Part IV.3 Archival Documents Related to the pli cacheté: B. Bru, Introduction to Doeblin’s “Sur la solution de M. Hostinský de l’équation de Chapman”.- W. Doeblin, Sur la solution de M. Hostinský de l’équation de Chapman [1940h/1993].- W.Doeblin (with an introduction by B. Bru and E. Seneta), Le cahier jaune: Recherche sur l’équation de Chapman. Propriétés communes aux mouvements régis par l’équation de Chapman [1940i/2020].- Part V Appendix: B. Bru and E. Seneta, Postface.- Acknowledgements.- Credits.- Bibliography.- Supplementary Reading.
£71.24
Springer International Publishing AG Design and Analysis of Experiments
Book SynopsisThis book offers a step-by-step guide to the experimental planning process and the ensuing analysis of normally distributed data, emphasizing the practical considerations governing the design of an experiment. Data sets are taken from real experiments and sample SAS programs are included with each chapter. Experimental design is an essential part of investigation and discovery in science; this book will serve as a modern and comprehensive reference to the subject.Trade Review“The textbook provides a practically oriented version of design and analysis of experiments. The corresponding methods are illustrated by means of numerous simple experiments. Thus, the models and methods are equipped with many examples, exercises, numerical results and related tables and figures. ... The present volume can be recommended as textbook for lectures on models and methods of experimental design as well as handbook for use in practice.” (Kurt Marti, zbMATH 1383.62001, 2018)Table of ContentsPrinciples and Techniques.- Planning Experiments.- Designs With One Source of Variation.- Inferences for Contrasts and Treatment Means.- Checking Model Assumptions.- Experiments With Two Crossed Treatment Factors.- Several Crossed Treatment Factors.- Polynomial Regression.- Analysis of Covariance.- Complete Block Designs.- Incomplete Block Designs.- Designs With Two Blocking Factors.- Confounded Two-Level Factorial Experiments.- Confounding in General Factorial Experiments.- Fractional Factorial Experiments.- Response Surface Methodology.- Random Effects and Variance Components.- Nested Models.- Split-Plot Designs
£104.49
Springer International Publishing AG Discrete Probability Models and Methods: Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding
Book SynopsisThe emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Chernoff's bound, Hoeffding's inequality, Holley's inequality) whose domain of application extends far beyond the present text. Although the examples treated in the book relate to the possible applications, in the communication and computing sciences, in operations research and in physics, this book is in the first instance concerned with theory. The level of the book is that of a beginning graduate course. It is self-contained, the prerequisites consisting merely of basic calculus (series) and basic linear algebra (matrices). The reader is not assumed to be trained in probability since the first chapters give in considerable detail the background necessary to understand the rest of the book.Trade Review“This is a book that any discrete proababilist will want to have on the shelf. It is a comprehensive extension of the author's masterfully written text Markov Chains ... Surprisingly; the book contains an extensive amount of information theory. ... In my opinion the new book would be ideal for a year-long course on discrete probability.” (Yevgeniy Kovchegov, Mathematical Reviews, May, 2018)“This is a very carefully and well-written book. The real pleasure comes from the contents but also from the excellent fonts and layout. Graduate university students and their teachers can benefit a lot of reading and using this book. There are more than good reasons to strongly recommend the book to anybody studying, teaching and/or researching in probability and its applications.” (Jordan M. Stoyanov, zbMATH 1386.60003, 2018) “This book is an excellent piece of writing. It has the strictness of a mathematical book whose traditional purpose is to state and prove theorems, and also has the features of a book on an engineering topic, where solved and unsolved exercises are provided. I appreciated the very carefully selected solved examples that are interwoven in each chapter. They provide an indispensable aid to digest the concepts and methods presented.” (Dimitrios Katsaros, Computing Reviews, February, 21, 2018) “This is a comprehensive volume on the application of discrete probability to combinatorics, information theory, and related fields. It is accessible for first-year graduate students. … Results are easy to find and reasonably easy to understand. … Summing Up: Recommended. Graduate students and faculty.” (M. Bona, Choice, Vol. 54 (12), August, 2017)Table of ContentsIntroduction.- 1.Events and probability.- 2.Random variables.- 3.Bounds and inequalities.- 4.Almost-sure convergence.- 5.Coupling and the variation distance.- 6.The probabilistic method.- 7.Codes and trees.- 8.Markov chains.- 9.Branching trees.- 10.Markov fields on graphs.- 11.Random graphs.- 12.Recurrence of Markov chains.- 13.Random walks on graphs.- 14.Asymptotic behaviour of Markov chains.- 15.Monte Carlo sampling.- 16. Convergence rates.- Appendix.- Bibliography.
£62.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Teubner-Taschenbuch der Stochastik:
Book SynopsisDieses umfassende Lehr-und Nachschlagewerk für Naturwissenschaftler und Ingenieure vermittelt dem Leser zentrale Teile der Wahrscheinlichkeitstheorie, der Theorie stochastischer Prozesse sowie der mathematischen Statistik.Table of Contents0 Einführung.- 1 Wahrscheinlichkeitstheorie.- 1.1 Zufällige Ereignisse.- 1.2 Wahrscheinlichkeit zufälliger Ereignisse.- 1.3 Bedingte Wahrscheinlichkeit und Unabhängigkeit.- 1.4 Diskrete Zufallsgrößen.- 1.4.1 Grundlagen.- 1.4.2 Parametrische Kenngrößen.- 1.4.3 Diskrete Wahrscheinlichkeitsverteilungen.- 1.4.4 Momenterzeugende Funktionen.- 1.5 Stetige Zufallsgrößen.- 1.5.1 Grundlagen.- 1.5.2 Parametrische Kenngrößen.- 1.5.3 Nichtnegative Zufallsgrößen.- 1.5.4 Stetige Wahrscheinlichkeitsverteilungen.- 1.5.4.1 Normalverteilung (Gaußsche Verteilung).- 1.5.4.2 Logarithmische Normalverteilung.- 1.5.4.3 Inverse Gaußverteilung.- 1.5.4.4 Weibuliverteilung.- 1.5.4.5 Erlangverteilung.- 1.5.4.6 Gammaverteilung.- 1.5.4.7 Betaverteilung.- 1.5.5 Momenterzeugende Funktionen.- 1.6 Funktionen einer Zufallsgröße.- 1.7 Simulation von Zufallsgrößen.- 1.8 Mehrdimensionale Zufallsgrößen.- 1.8.1 Zweidimensionale Zufallsgrößen.- 1.8.1.1 Gemeinsame Wahrscheinlichkeitsverteilung.- 1.8.1.2 Unabhängige Zufallsgrößen.- 1.8.1.3 Bedingte Verteilung.- 1.8.1.4 Funktionen zweier Zufallsgrößen.- 1.8.1.5 Abhängigkeitsmaße für zwei Zufallsgrößen.- 1.8.1.6 Zweidimensionale Normalverteilung.- 1.8.1.7 Diskrete zweidimensionale Zufallsgrößen.- 1.8.2 n-dimensionale Zufallsgrößen.- 1.8.2.1 Grundlagen.- 1.8.2.2 Summen von Zufallsgrößen.- 1.8.2.3 n-dimensionale Normalverteilung.- 1.9 Ungleichungen in der Wahrscheinlichkeitstheorie.- 1.9.1 Abschätzungen für Wahrscheinlichkeiten.- 1.9.1.1 Ungleichungen vom Markov-Tschebyschev-Typ.- 1.9.1.2 Exponentialabschätzungen.- 1.9.1.3 Ungleichungen fur Maxima von Summen.- 1.9.2 Ungleichungen und Abschätzungen für Momente.- 1.10 Grenzwertsätze in der Wahrscheinlichkeitstheorie.- 1.10.1 Konvergenzarten.- 1.10.2 Gesetze der großen Zahlen.- 1.10.2.1 Schwache Gesetze der großen Zahlen.- 1.10.2.2 Starke Gesetze der großen Zahlen.- 1.10.3 Zentraler Grenzwertsatz.- 1.10.4 Lokale Grenzwertsätze.- 1.11 Charakteristische Funktionen.- 1.11.1 Komplexe Zufallsgrößen.- 1.11.2 Eigenschaften charakteristischer Funktionen.- 1.11.3 Charakteristische Funktion diskreter Zufallsgrößen.- 2 Stochastische Prozesse.- 2.1 Einführung.- 2.2 Kenngrößen stochastischer Prozesse.- 2.3 Eigenschaften stochastischer Prozesse.- 2.4 Spezielle stochastische Prozesse.- 2.4.1 Stochastische Prozesse mit stetiger Zeit.- 2.4.2 Stochastische Prozesse mit diskreter Zeit.- 2.5 Poissonsche Prozesse.- 2.5.1 Homogener Poissonprozess.- 2.5.1.1 Definition und Eigenschaften.- 2.5.1.2 Homogener Poissonprozess und Gleichverteilung.- 2.5.2 Inhomogener Poissonprozess.- 2.6 Erneuerungsprozesse.- 2.6.1 Grundlagen.- 2.6.2 Erneuerungsfunktion.- 2.6.2.1 Erneuerungsgleichungen.- 2.6.2.2 Abschätzungen der Erneuerungsfunktion.- 2.6.3 Rekurrenzzeiten.- 2.6.4 Asymptotisches Verhalten.- 2.6.5 Stationäre Erneuerungsprozesse.- 2.6.6 Alternierende Erneuerungsprozesse.- 2.6.7 Kumulative stochastische Prozesse.- 2.6.8 Regenerative stochastische Prozesse.- 2.7 Markovsche Ketten mit diskreter Zeit.- 2.7.1 Grundlagen und Beispiele.- 2.7.2 Klassifikation der Zustände.- 2.7.2.1 Abgeschlossene Zustandsmengen.- 2.7.2.2 Äquivalenzklassen.- 2.7.2.3 Periodizität.- 2.7.2.4 Rekurrenz und Transienz.- 2.7.3 Grenzwertsätze und stationäre Verteilung.- 2.7.4 Geburts- und Todesprozesse.- 2.8 Markovsche Ketten mit stetiger Zeit.- 2.8.1 Grundlagen.- 2.8.2 Kolmogorovsche Gleichungen.- 2.8.3 Stationäre Zustandswahrscheinlichkeiten.- 2.8.4 Konstruktion Markovscher Systeme.- 2.8.5 Erlangsche Phasenmethode.- 2.8.6 Geburts- und Todesprozesse.- 2.8.6.1 Zeitabhängige Zustandswahrscheinlichkeiten.- 2.8.6.2 Stationäre Zustandswahrscheinlichkeiten.- 2.8.6.3 Verweildauern.- 2.8.7 Semi-Markovsche Prozesse.- 2.9 Martingale.- 2.9.1 Martingale in diskreter Zeit.- 2.9.2 Martingale in stetiger Zeit.- 2.10 Wiener Prozess.- 2.10.1 Definition und Eigenschaften.- 2.10.2 Niveauüberschreitung.- 2.10.3 Transformationen des Wiener Prozesses.- 2.10.3.1 Elementare Transformationen.- 2.10.3.2 Ornstein-Uhlenbeck-Prozess.- 2.10.3.3 Wiener Prozess mit Drift.- 2.10.3.4 Integraltransformationen.- 2.11 Spektralanalyse stationärer Prozesse.- 2.11.1 Grundbegriffe.- 2.11.2 Prozesse mit diskretem Spektrum.- 2.11.3 Prozesse mit stetigem Spektrum.- 2.11.3.1 Spektralzerlegung der Kovarianzfunktion.- 2.11.3.2 Spektralzerlegung des Prozesses.- 3 Mathematische Statistik.- 3.1 Stichproben und ihre empirische Auswertung.- 3.1.1 Stichproben.- 3.1.2 Häufigkeits- und Summenhäufigkeitsverteilung.- 3.1.3 Empirische Punktschätzung.- 3.1.3.1 Mittelwertsmaße.- 3.1.3.2 Streuungsmaße.- 3.1.4 Graphische Anpassung einer empirischen Verteilung an eine theoretische Verteilung.- 3.2 Punktschätzung.- 3.2.1 Eigenschaften von Schätzfunktionen.- 3.2.2 Schätzmethoden.- 3.2.2.1 Maximum-Likelihood-Methode.- 3.2.2.2 Momentenmethode.- 3.2.3 Wahrscheinlichkeitsverteilungen von Schätzfunktionen.- 3.2.3.1 Stichprobenverteilungen.- 3.2.3.2 Extremwertverteilungen.- 3.3 Intervallschätzung.- 3.3.1 Grundlagen.- 3.3.2 Konfidenzintervalle für Parameter der Normalverteilung.- 3.3.2.1 Konfidenzintervall für den Erwartungswert (Varianz bekannt).- 3.3.2.2 Konfidenzintervall für den Erwartungswert (Varianz unbekannt).- 3.3.2.3 Konfidenzintervall für die Varianz.- 3.3.3 Approximative Konfidenzintervalle.- 3.3.3.1 Konfidenzintervall für eine Wahrscheinlichkeit.- 3.3.3.2 Konfidenzintervall für den Erwartungswert einer poissonverteilten Zufallsgröße.- 3.4 Parametertests.- 3.4.1 Grundlagen.- 3.4.2 Tests über Parameter der Normalverteilung.- 3.4.2.1 Test über den Erwartungswert bei bekannter Varianz.- 3.4.2.2 Test über den Erwartungswert bei unbekannter Varianz.- 3.4.2.3 t-Test für verbundene Stichproben.- 3.4.2.4 Test auf Gleichheit der Erwartungswerte zweier Zufallsgrößen.- 3.4.2.5 Test auf Gleichheit der Varianzen.- 3.4.3 Approximative Tests.- 3.4.3.1 Test über eine Wahrscheinlichkeit.- 3.4.3.2 Vergleich zweier Wahrscheinlichkeiten.- 3.5 Verteilungsfreie Tests.- 3.5.1 Anpassungstests.- 3.5.1.1 Chi-Quadrat-Anpassungstest.- 3.5.1.2 Kolmogorov-Smirnov-Test.- 3.5.2 Tests auf Homogenität.- 3.5.2.1 Vorzeichentest.- 3.5.2.2 Wilcoxon-Vorzeichen-Rang-Test.- 3.5.2.3 Zwei-Stichproben-Rang-Test von Wilcoxon (-Mann-Whitney).- 3.5.2.4 Zwei-Stichproben-Iterationstest von Wald-Wolfowitz.- 3.5.2.5 Chi-Quadrat-Homogenitätstest.- 3.5.3 Chi-Quadrat-Unabhängigkeitstest.- 3.6 Korrelationsanalyse.- 3.6.1 Einführung.- 3.6.2 Einfacher Korrelationskoeffizient.- 3.6.3 Rangkorrelationskoeffizient von Spearman.- 3.7 Regressionsanalyse.- 3.7.1 Einführung.- 3.7.2 Einfache lineare Regression.- 3.7.2.1 Punktschätzung der Modellparameter.- 3.7.2.2 Konfidenz- und Prognoseintervalle.- 3.7.2.3 Tests über Regressionskoeffizienten und Anpassung.- 3.7.3 Nichtlineare Regressionsfunktion.- 3.7.3.1 Polynomiale Regressionsfunktion.- 3.7.3.2 Exponentielle Regressionsfunktion.- 3.7.4 Mehrfache lineare Regression.- 3.7.4.1 Punktschätzung der Modellparameter.- 3.7.4.2 Tests über Modellparameter.- 3.7.4.3 Konfidenz- und Prognoseintervalle.- 3.7.4.4 Abhängigkeits- und Prognosemaße.- 3.7.4.5 Voraussetzungen und funktionell richtiger Ansatz.- 3.7.4.6 Multikollinearität.- 3.7.4.7 Dominante Beobachtungen, Ausreißer, robuste Regression.- 3.7.4.8 Auswahl der Einflussgrößen.- 3.8 Multivariate Analyseverfahren.- 3.8.1 Grundbegriffe.- 3.8.2 Multivariate Varianzanalyse.- 3.8.2.1 Tests über Vektoren von Erwartungswerten.- 3.8.2.2 Das multivariate lineare Modell.- 3.8.2.3 Tests über Varianzstrukturen.- 3.8.3 Hauptkomponenten- und Faktoranalyse.- 3.8.3.1 Hauptkomponentenanalysen.- 3.8.3.2 Faktoranalyse.- 3.8.4 Diskrimination und Klassifikation.- 3.8.5 Clusteranalyse.- 3.8.5.1 Punktwolken und Distanzwahl.- 3.8.5.2 Zielfunktionen und Verfahrenstypen.- 3.8.5.3 Dendrogramme.- 3.8.6 Multidimensionale Skalierung.- 3.9 Statistische Versuchsplanung.- 3.9.1 Einführung.- 3.9.2 Optimale Versuchspläne.- 3.9.3 Faktorielle Versuchspläne.- 3.9.3.1 Grundlagen.- 3.9.3.2 Vollständige zweistufige faktorielle Versuchspläne.- 3.9.3.3 Teilweise zweistufige faktorielle Versuchspläne.- 3.9.3.4 Blockbildung in faktoriellen Versuchsplänen.- 3.9.3.5 Ergebnisverbesserung vermittels der Methode von Box-Wilson.- 3.10 Statistische Methoden in der Prozesskontrolle.- 3.10.1 Grundlagen.- 3.10.2 Shewart-Kontrollkarten.- 3.10.2.1 ?X- und R- Kontrollkarten.- 3.10.2.2 Kontrollkarten für Einzelmessungen.- 3.10.2.3 Kontrollkarten für die Gut-Schlecht-Prüfung.- 3.10.3 CUSUM-Kontrollkarten.- 3.10.4 EWMA-Kontrollkarten.- Tafeln.- Tafel I Verteilungsfunktion der standardisierten Normalverteilung.- Tafel III Quantile der Chi-Quadrat-Verteilung.- Tafel V Quantile der Testfunktion für den Kolmogorov-Smirnov-Test.- Tafel VIa Kritische Werte für den Zwei-Stichproben-Rang-Test von Wilcoxon (? = 0,01).- Tafel VIb Kritische Werte für den Zwei-Stichproben-Rang-Test von Wilcoxon (? = 0,05).- Tafel VII Kritische Werte für den Zwei-Stichproben-Iterationstest.- Tafel VIII Faktoren für die Konstruktion von Kontrollkarten.- Tafel IX Diskrete Wahrscheinlichkeitsverteilungen.- Tafel X Stetige Wahrscheinlichkeitsverteilungen.- Tafel XI Konfidenzintervalle.- Tafel XII Parametertests.- Literatur.
£28.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG An Introduction to Infinite-Dimensional Analysis
Book SynopsisBased on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate basic stochastic dynamical systems and Markov semi-groups, paying attention to their long-time behavior.Trade ReviewFrom the reviews: "This is an extended version of the author’s ‘An introduction to infinite-dimensional analysis’ published by Scuola Normale Superiore, Pisa … . A well written textbook (even an introductory research monograph), suitable for teaching a graduate course." (Neils Jacob, Zentralblatt MATH, Vol. 1109 (11), 2007) "The present volume collects together … the notes of the course on infinite-dimensional analysis held by the author at the Scuola Normale Superiore of Pisa in recent years. The book is intended for people who have some knowledge of functional analysis … . It provides an extremely useful tool for those scholars who are interested in learning some basics about Gaussian measures in Hilbert spaces, Brownian motion, Markov transition semigroups … . The book is well written and all arguments are clearly and rigorously presented." (Sandra Cerrai, Mathematical Reviews, Issue 2009 a)Table of ContentsGaussian measures in Hilbert spaces.- The Cameron–Martin formula.- Brownian motion.- Stochastic perturbations of a dynamical system.- Invariant measures for Markov semigroups.- Weak convergence of measures.- Existence and uniqueness of invariant measures.- Examples of Markov semigroups.- L2 spaces with respect to a Gaussian measure.- Sobolev spaces for a Gaussian measure.- Gradient systems.
£44.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG The Fokker-Planck Equation: Methods of Solution and Applications
Book SynopsisThis is the first textbook to include the matrix continued-fraction method, which is very effective in dealing with simple Fokker-Planck equations having two variables. Other methods covered are the simulation method, the eigen-function expansion, numerical integration, and the variational method. Each solution is applied to the statistics of a simple laser model and to Brownian motion in potentials. The whole is rounded off with a supplement containing a short review of new material together with some recent references. This new study edition will prove to be very useful for graduate students in physics, chemical physics, and electrical engineering, as well as for research workers in these fields.Table of Contents1. Introduction.- 1.1 Brownian Motion.- 1.1.1 Deterministic Differential Equation.- 1.1.2 Stochastic Differential Equation.- 1.1.3 Equation of Motion for the Distribution Function.- 1.2 Fokker-Planck Equation.- 1.2.1 Fokker-Planck Equation for One Variable.- 1.2.2 Fokker-Planck Equation for N Variables.- 1.2.3 How Does a Fokker-Planck Equation Arise?.- 1.2.4 Purpose of the Fokker-Planck Equation.- 1.2.5 Solutions of the Fokker-Planck Equation.- 1.2.6 Kramers and Smoluchowski Equations.- 1.2.7 Generalizations of the Fokker-Planck Equation.- 1.3 Boltzmann Equation.- 1.4 Master Equation.- 2. Probability Theory.- 2.1 Random Variable and Probability Density.- 2.2 Characteristic Function and Cumulants.- 2.3 Generalization to Several Random Variables.- 2.3.1 Conditional Probability Density.- 2.3.2 Cross Correlation.- 2.3.3 Gaussian Distribution.- 2.4 Time-Dependent Random Variables.- 2.4.1 Classification of Stochastic Processes.- 2.4.2 Chapman-Kolmogorov Equation.- 2.4.3 Wiener-Khintchine Theorem.- 2.5 Several Time-Dependent Random Variables.- 3. Langevin Equations.- 3.1 Langevin Equation for Brownian Motion.- 3.1.1 Mean-Squared Displacement.- 3.1.2 Three-Dimensional Case.- 3.1.3 Calculation of the Stationary Velocity Distribution Function.- 3.2 Ornstein-Uhlenbeck Process.- 3.2.1 Calculation of Moments.- 3.2.2 Correlation Function.- 3.2.3 Solution by Fourier Transformation.- 3.3 Nonlinear Langevin Equation, One Variable.- 3.3.1 Example.- 3.3.2 Kramers-Moyal Expansion Coefficients.- 3.3.3 Itô’s and Stratonovich’s Definitions.- 3.4 Nonlinear Langevin Equations, Several Variables.- 3.4.1 Determination of the Langevin Equation from Drift and Diffusion Coefficients.- 3.4.2 Transformation of Variables.- 3.4.3 How to Obtain Drift and Diffusion Coefficients for Systems.- 3.5 Markov Property.- 3.6 Solutions of the Langevin Equation by Computer Simulation.- 4. Fokker-Planck Equation.- 4.1 Kramers-Moyal Forward Expansion.- 4.1.1 Formal Solution.- 4.2 Kramers-Moyal Backward Expansion.- 4.2.1 Formal Solution.- 4.2.2 Equivalence of the Solutions of the Forward and Backward Equations.- 4.3 Pawula Theorem.- 4.4 Fokker-Planck Equation for One Variable.- 4.4.1 Transition Probability Density for Small Times.- 4.4.2 Path Integral Solutions.- 4.5 Generation and Recombination Processes.- 4.6 Application of Truncated Kramers-Moyal Expansions.- 4.7 Fokker-Planck Equation for N Variables.- 4.7.1 Probability Current.- 4.7.2 Joint Probability Distribution.- 4.7.3 Transition Probability Density for Small Times.- 4.8 Examples for Fokker-Planck Equations with Several Variables.- 4.8.1 Three-Dimensional Brownian Motion without Position Variable.- 4.8.2 One-Dimensional Brownian Motion in a Potential.- 4.8.3 Three-Dimensional Brownian Motion in an External Force.- 4.8.4 Brownian Motion of Two Interacting Particles in an External Potential.- 4.9 Transformation of Variables.- 4.10 Covariant Form of the Fokker-Planck Equation.- 5. Fokker-Planck Equation for One Variable; Methods of Solution.- 5.1 Normalization.- 5.2 Stationary Solution.- 5.3 Ornstein-Uhlenbeck Process.- 5.4 Eigenfunction Expansion.- 5.5 Examples.- 5.5.1 Parabolic Potential.- 5.5.2 Inverted Parabolic Potential.- 5.5.3 Infinite Square Well for the Schrüdinger Potential.- 5.5.4 V-Shaped Potential for the Fokker-Planck Equation.- 5.6 Jump Conditions.- 5.7 A Bistable Model Potential.- 5.8 Eigenfunctions and Eigenvalues of Inverted Potentials.- 5.9 Approximate and Numerical Methods for Determining Eigenvalues and Eigenfunctions.- 5.9.1 Variational Method.- 5.9.2 Numerical Integration.- 5.9.3 Expansion into a Complete Set.- 5.10 Diffusion Over a Barrier.- 5.10.1 Kramers’ Escape Rate.- 5.10.2 Bistable and Metastable Potential.- 6. Fokker-Planck Equation for Several Variables; Methods of Solution.- 6.1 Approach of the Solutions to a Limit Solution.- 6.2 Expansion into a Biorthogonal Set.- 6.3 Transformation of the Fokker-Planck Operator, Eigenfunction Expansions.- 6.4 Detailed Balance.- 6.5 Ornstein-Uhlenbeck Process.- 6.6 Further Methods for Solving the Fokker-Planck Equation.- 6.6.1 Transformation of Variables.- 6.6.2 Variational Method.- 6.6.3 Reduction to an Hermitian Problem.- 6.6.4 Numerical Integration.- 6.6.5 Expansion into Complete Sets.- 6.6.6 Matrix Continued-Fraction Method.- 6.6.7 WKB Method.- 7. Linear Response and Correlation Functions.- 7.1 Linear Response Function.- 7.2 Correlation Functions.- 7.3 Susceptibility.- 8. Reduction of the Number of Variables.- 8.1 First-Passage Time Problems.- 8.2 Drift and Diffusion Coefficients Independent of Some Variables.- 8.2.1 Time Integrals of Markovian Variables.- 8.3 Adiabatic Elimination of Fast Variables.- 8.3.1 Linear Process with Respect to the Fast Variable.- 8.3.2 Connection to the Nakajima-Zwanzig Projector Formalism.- 9. Solutions of Tridiagonal Recurrence Relations, Application to Ordinary and Partial Differential Equations.- 9.1 Applications and Forms of Tridiagonal Recurrence Relations.- 9.1.1 Scalar Recurrence Relation.- 9.1.2 Vector Recurrence Relation.- 9.2 Solutions of Scalar Recurrence Relations.- 9.2.1 Stationary Solution.- 9.2.2 Initial Value Problem.- 9.2.3 Eigenvalue Problem.- 9.3 Solutions of Vector Recurrence Relations.- 9.3.1 Initial Value Problem.- 9.3.2 Eigenvalue Problem.- 9.4 Ordinary and Partial Differential Equations with Multiplicative Harmonic Time-Dependent Parameters.- 9.4.1 Ordinary Differential Equations.- 9.4.2 Partial Differential Equations.- 9.5 Methods for Calculating Continued Fractions.- 9.5.1 Ordinary Continued Fractions.- 9.5.2 Matrix Continued Fractions.- 10. Solutions of the Kramers Equation.- 10.1 Forms of the Kramers Equation.- 10.1.1 Normalization of Variables.- 10.1.2 Reversible and Irreversible Operators.- 10.1.3 Transformation of the Operators.- 10.1.4 Expansion into Hermite Functions.- 10.2 Solutions for a Linear Force.- 10.2.1 Transition Probability.- 10.2.2 Eigenvalues and Eigenfunctions.- 10.3 Matrix Continued-Fraction Solutions of the Kramers Equation.- 10.3.1 Initial Value Problem.- 10.3.2 Eigenvalue Problem.- 10.4 Inverse Friction Expansion.- 10.4.1 Inverse Friction Expansion for K0(t), G0,0(t) and L0(t).- 10.4.2 Determination of Eigenvalues and Eigenvectors.- 10.4.3 Expansion for the Green’s Function Gn,m(t).- 10.4.4 Position-Dependent Friction.- 11. Brownian Motion in Periodic Potentials.- 11.1 Applications.- 11.1.1 Pendulum.- 11.1.2 Superionic Conductor.- 11.1.3 Josephson Tunneling Junction.- 11.1.4 Rotation of Dipoles in a Constant Field.- 11.1.5 Phase-Locked Loop.- 11.1.6 Connection to the Sine-Gordon Equation.- 11.2 Normalization of the Langevin and Fokker-Planck Equations.- 11.3 High-Friction Limit.- 11.3.1 Stationary Solution.- 11.3.2 Time-Dependent Solution.- 11.4 Low-Friction Limit.- 11.4.1 Transformation to E and x Variables.- 11.4.2 ‘Ansatz’ for the Stationary Distribution Functions.- 11.4.3 x-Independent Functions.- 11.4.4 x-Dependent Functions.- 11.4.5 Corrected x-Independent Functions and Mobility.- 11.5 Stationary Solutions for Arbitrary Friction.- 11.5.1 Periodicity of the Stationary Distribution Function.- 11.5.2 Matrix Continued-Fraction Method.- 11.5.3 Calculation of the Stationary Distribution Function.- 11.5.4 Alternative Matrix Continued Fraction for the Cosine Potential.- 11.6 Bistability between Running and Locked Solution.- 11.6.1 Solutions Without Noise.- 11.6.2 Solutions With Noise.- 11.6.3 Low-Friction Mobility With Noise.- 11.7 Instationary Solutions.- 11.7.1 Diffusion Constant.- 11.7.2 Transition Probability for Large Times.- 11.8 Susceptibilities.- 11.8.1 Zero-Friction Limit.- 11.9 Eigenvalues and Eigenfunctions.- 11.9.1 Eigenvalues and Eigenfunctions in the Low-Friction Limit.- 12. Statistical Properties of Laser Light.- 12.1 Semiclassical Laser Equations.- 12.1.1 Equations Without Noise.- 12.1.2 Langevin Equation.- 12.1.3 Laser Fokker-Planck Equation.- 12.2 Stationary Solution and Its Expectation Values.- 12.3 Expansion in Eigenmodes.- 12.4 Expansion into a Complete Set; Solution by Matrix Continued Fractions.- 12.4.1 Determination of Eigenvalues.- 12.5 Transient Solution.- 12.5.1 Eigenfunction Method.- 12.5.2 Expansion into a Complete Set.- 12.5.3 Solution for Large Pump Parameters.- 12.6 Photoelectron Counting Distribution.- 12.6.1 Counting Distribution for Short Intervals.- 12.6.2 Expectation Values for Arbitrary Intervals.- Appendices.- A1 Stochastic Differential Equations with Colored Gaussian Noise.- A2 Boltzmann Equation with BGK and SW Collision Operators.- A3 Evaluation of a Matrix Continued Fraction for the Harmonic Oscillator.- A4 Damped Quantum-Mechanical Harmonic Oscillator.- A5 Alternative Derivation of the Fokker-Planck Equation.- A6 Fluctuating Control Parameter.- S. Supplement to the Second Edition.- S.1 Solutions of the Fokker-Planck Equation by Computer Simulation (Sect. 3.6).- S.2 Kramers-Moyal Expansion (Sect. 4.6).- S.3 Example for the Covariant Form of the Fokker-Planck Equation (Sect. 4.10).- S.4 Connection to Supersymmetry and Exact Solutions of the One Variable Fokker-Planck Equation (Chap. 5).- S.5 Nondifferentiability of the Potential for the Weak Noise Expansion (Sects. 6.6 and 6.7).- S.6 Further Applications of Matrix Continued-Fractions (Chap. 9).- S.7 Brownian Motion in a Double-Well Potential (Chaps. 10 and 11).- S.8 Boundary Layer Theory (Sect. 11.4).- S.9 Calculation of Correlation Times (Sect. 7.12).- S.10 Colored Noise (Appendix A1).- S.11 Fokker-Planck Equation with a Non-Positive-Definite Diffusion Matrix and Fokker-Planck Equation with Additional Third-Order-Derivative Terms.- References.
£66.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Introduction to the Statistical Analysis of Categorical Data
Book Synopsisto the Statistical Analysis of Categorical Data With 16 Figures and 121 Tables , Springer Prof. Erling B. Andersen University of Copenhagen Department of Statistics 6 Studiestrrede DK-14SS Copenhagen Denmark ISBN 978-3-540-62399-1 CataJoging-in-Publication Data applied ror Oie Oeutsche Bibliothek - CIP-Einheitsaufnahme Andersen, Erling B. : Introduction to the statistical analysis of categorical data analysis: with 121 tables I Erling B. Andersen. -Berlin; Heidelberg; New York; Bucelona; Buda- pest; Hong Kong; London; Milan; Paris; Santa Clara; Singapore; Tokyo: Springer, 1997 ISBN 978-3-540~2399-1 ISBN 978-3~2-59123-5 (eBook) DOI10. 1007/978-3~2-59123-5 This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any o!her way, and storage in data banks. Ouplication of this publication or parts thereof IS permitted only under the provisions of !he German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under !he German Copyright Law. O Springer-Verlag Berlin Heidelberg 1997 Originally published by Springer-Verlag Berlin Heidelberg New York in 1997 The use of general descriptive names, registered names, trademarks, etc. in this publi- cation does not imply, even in !he absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and !herefore free for general use.Table of ContentsIntroduction: The two-way Table.- Basic Theory: Exponential families; Statistical inference in an exponential family; The binomial distribution; The Poisson distribution; Composite hypotheses; Applications to the multinomial distribution; Log-linear models; The two-way contingency table; The numerical solution of the likelihood equations for the log-linear model.- Three-way contingency tables: Log-linear models; Log-linear hypotheses; Estimation; testing hypotheses; Interpretation of the log-linear parameters; Choice of model; Detection of model deviations.- Multi-dimensional contingency tables: The log-linear-model; Classification and interpretation of log-linear models; Choice of model; Diagnostics; Model search strategies.- Incomplete Tables: Random and structural zeros; Counting th number of degrees of freedom; Validity of the X2-approximation.- The Logit Model: The Logit model; Hypothesis testing in the logit model; Logit models with higher order interactions; The Logit model as a regression model.- Logistic Regression Analysis: The logistic regression model; Estimation in the logistic regression model; Numerical solution of the likelihood equations; Checking the fit of the model; Hypothesis testing; Diagnostics; Predictions; Dummy variables; Polytomous response variables.- Association Models: Symmetry models; Marginal homogeneity; RC-association models; Correspondence analysis.- Appendix: Solutions and output to selected excercises.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Risk and Meaning: Adversaries in Art, Science and
Book SynopsisThis richly illustrated book is an exploration of how chance and risk, on the one hand, and meaning or significance on the other, compete for the limelight in art, in philosophy, and in science. In modern society, prudence and probability calculation permeate our daily lives. Yet it is clear for all to see that neither cautious bank regulations nor mathematics have prevented economic crises from occurring time and again. Nicolas Bouleau argues that it is the meaning we assign to an event that determines the perceived risk, and that we generally turn a blind eye to this important fact, because the word "meaning" is itself awkward to explain. He tackles this fundamental question through examples taken from cultural fields ranging from painting, architecture, and music, to poetry, biology, and astronomy. This enables the reader to view overwhelming risks in a different light. Bouleau clarifies that the most important thing in a time of uncertainty is to think of prudence on a higher level, one that truly addresses the various subjective interpretations of the world.Trade ReviewFrom the reviews:“Risk and Meaning is a quirky book, both in its topic and its physical layout and the writing style that the author adopts … . it is a book that is mathematics-adjacent, and I think that anyone who is able to get past (or even relish) some of the quirkiness in the book will certainly find themselves with plenty to think about. And I’m not sure what more one could ask for in a book.” (Darren Glass, The Mathematical Association of America, November, 2011)Table of ContentsEntrance: Interpretation and Paradigms.- I. Cicero and Divination.- II. Cournot’s "Philosophic Probabilities".- III. Mathematical Probabilities.- IV. Democracy by Chance.- V. Gestalt, Structure, Pattern.- VI. The Third Dimension of Risk.- VII. ''Modern" Architecture.- VIII. The Ideal City.- IX. Daring the Abstract in Art.- X. Saussure or the Dread of Mathematical Probabilities.- XI. Jacques Monod’s Roulette.- XII. From Fortuitism to Animism.- XIII. The Slip as Fortuity and Meaning.- XIV. Guessing Astronomy.- XV. The Legitimacy of Science and Love.- Hints and Index.
£38.24
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Collected Papers I: Limit Theorems
Book SynopsisFrom the Preface: Srinivasa Varadhan began his research career at the Indian Statistical Institute (ISI), Calcutta, where he started as a graduate student in 1959. His first paper appeared in Sankhyá, the Indian Journal of Statistics in 1962. Together with his fellow students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy, Varadhan began the study of probability on topological groups and on Hilbert spaces, and quickly gained an international reputation. At this time Varadhan realised that there are strong connections between Markov processes and differential equations, and in 1963 he came to the Courant Institute in New York, where he has stayed ever since. Here he began working with the probabilists Monroe Donsker and Marc Kac, and a graduate student named Daniel Stroock. He wrote a series of papers on the Martingale Problem and Diffusions together with Stroock, and another series of papers on Large Deviations together with Donsker. With this work Varadhan's reputation as one of the leading mathematicians of the time was firmly established. Since then he has contributed to several other areas of probability, analysis and physics, and collaborated with numerous distinguished mathematicians. Varadhan was awarded the Abel Prize in 2007. These Collected Works contain all his research papers over the half-century spanning 1962 to early 2012. Volume I includes the introductory material, the papers on limit theorems and review articles.Table of ContentsAutobiography: S. R. S. Varadhan.- Introduction: S. R. S. Varadhan.- Prize Citations.- Diffusion Theory by Daniel W. Stroock. - Large Deviations by Daniel W. Stroock.- Large Deviation and Homogenization by Fraydoun Rezakhanlou.- Varadhan's Work on Hydrodynamical Limits by Jeremy Quastel and Horng-Tzer Yau.- Book Review: Multidimensional Diffusion Processes by D. W. Stroock and S. R. S. Varadhan.- Limit Theorems: Limit theorems for sums of independent random variables with values in a Hilbert space.- On the category of indecomposable distributions on topological groups.- Probability distributions on locally compact abelian groups.- Extension of stationary stochastic processes.- Limit theorems in probability.- A limit theorem with strong mixing in Banach space and two applications to stochastic differential equations.- Limit theorems for random walks on Lie groups.- Martingale approach to some limit theorems.- Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions.- Bounding functions of Markov processes and the shortest queue problem.- Finite approximations to quantum systems.- Self-diffusion of a tagged particle in equilibrium for asymmetric mean zero random walk with simple exclusion.- Diffusive limit of a tagged particle in asymmetric simple exclusion processes.- A martingale proof of Dobrushin's theorem for non-homogeneous Markov chains.- Review Articles.- Diffusion processes, Stochastic processes: theory and methods.- Stochastic analysis and applications.- Large deviations and entropy, Entropy.- The role of weak convergence in probability theory.
£80.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Collected Papers II: PDE, SDE, Diffusions, Random
Book SynopsisFrom the Preface: Srinivasa Varadhan began his research career at the Indian Statistical Institute (ISI), Calcutta, where he started as a graduate student in 1959. His first paper appeared in Sankhyá, the Indian Journal of Statistics in 1962. Together with his fellow students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy, Varadhan began the study of probability on topological groups and on Hilbert spaces, and quickly gained an international reputation. At this time Varadhan realised that there are strong connections between Markov processes and differential equations, and in 1963 he came to the Courant Institute in New York, where he has stayed ever since. Here he began working with the probabilists Monroe Donsker and Marc Kac, and a graduate student named Daniel Stroock. He wrote a series of papers on the Martingale Problem and Diffusions together with Stroock, and another series of papers on Large Deviations together with Donsker. With this work Varadhan's reputation as one of the leading mathematicians of the time was firmly established. Since then he has contributed to several other areas of probability, analysis and physics, and collaborated with numerous distinguished mathematicians. Varadhan was awarded the Abel Prize in 2007. These Collected Works contain all his research papers over the half-century spanning 1962 to early 2012. Volume II includes the papers on PDE, SDE, diffusions, and random media.Table of ContentsVol. II: Diffusion processes with continuous coefficients - I (with D. W. Stroock).- Diffusion processes with continuous coefficients - II (with D. W. Stroock).- Diffusion processes with boundary conditions (with D. W. Stroock).- On degenerate elliptic-parabolic operators of second order and their associated diffusions (with D. W. Stroock).- On the support of diffusion processes with applications to the strong maximum principle (with D. W. Stroock).- Diffusion processes (with D. W. Stroock).- A probabilistic approach to Hp(Rd) (with D. W. Stroock).- Kac functional and Schrodinger equation (with K. L. Chung).- Brownian motion in a wedge with oblique reection (with R. J. Williams).- A multidimensional process involving local time (with A.S. Sznitman).- Etat fondamental et principe du maximum pour les operateurs elliptiques du second ordre dans des domaines generaux. [The ground state and maximum principle for second-order elliptic operators in general domains] (with H. Berestycki and L. Nirenberg).- The principal eigenvalue and maximum principle for second-order elliptic operators in general domains (with H. Berestycki and L. Nirenberg).- Diffusion semigroups and di_usion processes corresponding to degenerate divergence form operators (with J. Quastel).- Random Media.- Diffusion in regions with many small holes (with G. Papanicolaou).- Boundary value problems with rapidly oscillating random coefficients (with G. Papanicolaou).- Diffusions with random coefficients (with G. Papanicolaou).- Ohrnstein-Uhlenbeck process in a random potential (with G. Papanicolaou).- Large deviations for random walks in a random environment.- Random walks in a random environment.- Stochastic homogenization of Hamilton-Jacobi-Bellman equations (with E. Kosygina and F. Rezakhanlou).- Homogenization of Hamilton-Jacobi-Bellman equations with respect to time-space shifts in a stationary ergodic medium (with E. Kosygina).- Behavior of the solution of a random semilinear heat equation (with N. Zygouras).
£80.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Collected Papers III: Large Deviations
Book SynopsisFrom the Preface: Srinivasa Varadhan began his research career at the Indian Statistical Institute (ISI), Calcutta, where he started as a graduate student in 1959. His first paper appeared in Sankhyá, the Indian Journal of Statistics in 1962. Together with his fellow students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy, Varadhan began the study of probability on topological groups and on Hilbert spaces, and quickly gained an international reputation. At this time Varadhan realised that there are strong connections between Markov processes and differential equations, and in 1963 he came to the Courant Institute in New York, where he has stayed ever since. Here he began working with the probabilists Monroe Donsker and Marc Kac, and a graduate student named Daniel Stroock. He wrote a series of papers on the Martingale Problem and Diffusions together with Stroock, and another series of papers on Large Deviations together with Donsker. With this work Varadhan's reputation as one of the leading mathematicians of the time was firmly established. Since then he has contributed to several other areas of probability, analysis and physics, and collaborated with numerous distinguished mathematicians. Varadhan was awarded the Abel Prize in 2007. These Collected Works contain all his research papers over the half-century spanning 1962 to early 2012.Volume III includes the papers on large deviations. Table of ContentsLarge Deviations.- Asymptotic probabilities and differential equations.- On the behavior of the fundamental solution of the heat equation with variable coefficients .- Diffusion processes in a small time interval .- On a variational formula for the principal eigenvalue for operators with maximum principle.- Asymptotic evaluation of certain Markov process expectations for large time I.- Asymptotic evaluation of certain Markov process expectations for large time II.- Asymptotic evaluation of certain Wiener integrals for large time.- Asymptotics for the Wiener sausage.- Erratum: Asymptotics for the Wiener sausage.- Asymptotic evaluation of certain Markov process expectations for large time III.- On the principal eigenvalue of second-order elliptic differential operators.- On laws of the iterated logarithm for local times.- Some problems of large deviations.- On the number of distinct sites visited by a random walk.- A law of the iterated logarithm for total occupation times of transient Brownian motion.- Some problems of large deviations .- The polaron problem and large deviations.- Asymptotic evaluation of certain Markov process expectations for large time IV.- Asymptotics for the polaron.- Large deviations for stationary Gaussian processes.- Large deviations and applications.- Large deviations for non-interacting infinite-particle systems.- Some familiar examples for which the large deviation principle does not hold.- The large deviation principle for the Erdös-Rényi random graph.- Large deviations for random matrices.
£80.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Collected Papers IV: Particle Systems and Their
Book SynopsisFrom the Preface: Srinivasa Varadhan began his research career at the Indian Statistical Institute (ISI), Calcutta, where he started as a graduate student in 1959. His first paper appeared in Sankhyá, the Indian Journal of Statistics in 1962. Together with his fellow students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy, Varadhan began the study of probability on topological groups and on Hilbert spaces, and quickly gained an international reputation. At this time Varadhan realised that there are strong connections between Markov processes and differential equations, and in 1963 he came to the Courant Institute in New York, where he has stayed ever since. Here he began working with the probabilists Monroe Donsker and Marc Kac, and a graduate student named Daniel Stroock. He wrote a series of papers on the Martingale Problem and Diffusions together with Stroock, and another series of papers on Large Deviations together with Donsker. With this work Varadhan's reputation as one of the leading mathematicians of the time was firmly established. Since then he has contributed to several other areas of probability, analysis and physics, and collaborated with numerous distinguished mathematicians. Varadhan was awarded the Abel Prize in 2007. These Collected Works contain all his research papers over the half-century spanning 1962 to early 2012. Volume IV includes the papers on particle systems.Table of ContentsVolume 4: Particle Systems and Their Large Deviations.- Nonlinear diffusion limit for a system with nearest neighbor interaction.- Hydrodynamics and large deviation for simple exclusion processes.- Large deviations from a hydrodynamic scaling limit.- On the derivation of conservation laws for stochastic dynamics.- Scaling limits for interacting diffusions.- Scaling limit for interacting Ornstein-Uhlenbeck processes.- Entropy methods in hydrodynamical scaling.- Hydrodynamical limit for a Hamiltonian system with weak noise.- Nonlinear diffusion limit for a system with nearest neighbor interactions II.- Regularity of self-diffusion coefficient.- Entropy methods in hydrodynamic scaling.- Spectral gap for zero-range dynamics.- The complex story of simple exclusion.- Non-gradient models in hydrodynamic scaling.- Relative entropy and mixing properties of interacting particle systems.- Diffusive limit of lattice gas with mixing conditions.- Large deviations for the symmetric simple exclusion process in dimensions d > 3.- Large deviations for interacting particle systems.- Infinite particle systems and their scaling limits.- Lectures on hydrodynamic scaling.- Scaling limits of large interacting systems .- Asymptotic behavior of a tagged particle in simple exclusion processes.- Large deviation and hydrodynamic scaling.- Symmetric simple exclusion process: regularity of the self-diffusion coefficient.- Finite-dimensional approximation of the self-diffusion coefficient for the exclusion process.- Large deviations for the asymmetric simple exclusion process.- Diffusive behaviour of the equilibrium fluctuations in the asymmetric exclusion processes.- On viscosity and fluctuation-dissipation in exclusion processes.- Large deviations for the current and tagged particle in 1d nearest neighbor.- Symmetric simple exclusion.- List of Publications of S.R.S. Varadhan.- Acknowledgements.
£80.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Long-Memory Processes: Probabilistic Properties
Book SynopsisLong-memory processes are known to play an important part in many areas of science and technology, including physics, geophysics, hydrology, telecommunications, economics, finance, climatology, and network engineering. In the last 20 years enormous progress has been made in understanding the probabilistic foundations and statistical principles of such processes. This book provides a timely and comprehensive review, including a thorough discussion of mathematical and probabilistic foundations and statistical methods, emphasizing their practical motivation and mathematical justification. Proofs of the main theorems are provided and data examples illustrate practical aspects. This book will be a valuable resource for researchers and graduate students in statistics, mathematics, econometrics and other quantitative areas, as well as for practitioners and applied researchers who need to analyze data in which long memory, power laws, self-similar scaling or fractal properties are relevant.Trade ReviewFrom the book reviews:“This encyclopaedic book covers almost the whole literature on univariate and multivariate long-range dependent (LRD) processes, or long-memory processes or strongly dependent processes. … This volume is then of strong interest for both researchers and teachers familiar with the topic, as it gives an overall, structured and balanced picture of the current state of the art. Readers less familiar with the topic will easily find their way in the vast literature on this issue, and will have their curiosity satisfied.” (Gilles Teyssière, Mathematical Reviews, October, 2014)“This book aims to cover probabilistic and statistical aspects of long-memory processes in as much detail as possible, including a broad range of topics. The authors did an excellent job to reach their goals, and the book would be a must for researchers interested in long-memory processes and practioners on time series and data analysis. … the book is an excellent choice for anyone who is working in fields related to long-memory processes with many update information and research topics.” (Weiping Li, zbMATH, Vol. 1282, 2014)Table of ContentsDefinition of Long Memory.- Origins and Generation of Long Memory.- Mathematical Concepts.- Limit Theorems.- Statistical Inference for Stationary Processes.- Statistical Inference for Nonlinear Processes.- Statistical Inference for Nonstationary Processes.- Forecasting.- Spatial and Space-Time Processes.- Resampling.- Function Spaces.- Regularly Varying Functions.- Vague Convergence.- Some Useful Integrals.- Notation and Abbreviations.
£151.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG One-Dimensional Dynamics
Book SynopsisOne-dimensional dynamics has developed in the last decades into a subject in its own right. Yet, many recent results are inaccessible and have never been brought together. For this reason, we have tried to give a unified ac count of the subject and complete proofs of many results. To show what results one might expect, the first chapter deals with the theory of circle diffeomorphisms. The remainder of the book is an attempt to develop the analogous theory in the non-invertible case, despite the intrinsic additional difficulties. In this way, we have tried to show that there is a unified theory in one-dimensional dynamics. By reading one or more of the chapters, the reader can quickly reach the frontier of research. Let us quickly summarize the book. The first chapter deals with circle diffeomorphisms and contains a complete proof of the theorem on the smooth linearizability of circle diffeomorphisms due to M. Herman, J.-C. Yoccoz and others. Chapter II treats the kneading theory of Milnor and Thurstonj also included are an exposition on Hofbauer's tower construction and a result on fuB multimodal families (this last result solves a question posed by J. Milnor).Table of Contents0. Introduction.- I. Circle Diffeomorphisms.- 1. The Combinatorial Theory of Poincaré.- 2. The Topological Theory of Denjoy.- 2.a The Denjoy Inequality.- 2.b Ergodicity.- 3. Smooth Conjugacy Results.- 4. Families of Circle Diffeomorphisms; Arnol’d tongues.- 5. Counter-Examples to Smooth Linearizability.- 6. Frequency of Smooth Linearizability in Families.- 7. Some Historical Comments and Further Remarks.- II. The Combinatorics of One-Dimensional Endomorphisms.- 1. The Theorem of Sarkovskii.- 2. Covering Maps of the Circle as Dynamical Systems.- 3. The Kneading Theory and Combinatorial Equivalence.- 3.a Examples.- 3.b Hofbauer’s Tower Construction.- 4. Full Families and Realization of Maps.- 5. Families of Maps and Renormalization.- 6. Piecewise Monotone Maps can be Modelled by Polynomial Maps.- 7. The Topological Entropy.- 8. The Piecewise Linear Model.- 9. Continuity of the Topological Entropy.- 10. Monotonicity of the Kneading Invariant for the Quadratic Family.- 11. Some Historical Comments and Further Remarks.- III. Structural Stability and Hyperbolicity.- 1. The Dynamics of Rational Mappings.- 2. Structural Stability and Hyperbolicity.- 3. Hyperbolicity in Maps with Negative Schwarzian Derivative.- 4. The Structure of the Non-Wandering Set.- 5. Hyperbolicity in Smooth Maps.- 6. Misiurewicz Maps are Almost Hyperbolic.- 7. Some Further Remarks and Open Questions.- IV. The Structure of Smooth Maps.- 1. The Cross-Ratio: the Minimum and Koebe Principle.- l.a Some Facts about the Schwarzian Derivative.- 2. Distortion of Cross-Ratios.- 2.a The Zygmund Conditions.- 3. Koebe Principles on Iterates.- 4. Some Simplifications and the Induction Assumption.- 5. The Pullback of Space: the Koebe/Contraction Principle.- 6. Disjointness of Orbits of Intervals.- 7. Wandering Intervals Accumulate on Turning Points.- 8. Topological Properties of a Unimodal Pullback.- 9. The Non-Existence of Wandering Intervals.- 10. Finiteness of Attractors.- 11. Some Further Remarks and Open Questions.- V. Ergodic Properties and Invariant Measures.- 1. Ergodicity, Attractors and Bowen-Ruelle-Sinai Measures.- 2. Invariant Measures for Markov Maps.- 3. Constructing Invariant Measures by Inducing.- 4. Constructing Invariant Measures by Pulling Back.- 5. Transitive Maps Without Finite Continuous Measures.- 6. Frequency of Maps with Positive Liapounov Exponents in Families and Jakobson’s Theorem.- 7. Some Further Remarks and Open Questions.- VI. Renormalization.- 1. The Renormalization Operator.- 2. The Real Bounds.- 3. Bounded Geometry.- 4. The PullBack Argument.- 5. The Complex Bounds.- 6. Riemann Surface Laminations.- 7. The Almost Geodesic Principle.- 8. Renormalization is Contracting.- 9. Universality of the Attracting Cantor Set.- 10. Some Further Remarks and Open Questions.- VII. Appendix.- 1. Some Terminology in Dynamical Systems.- 2. Some Background in Topology.- 3. Some Results from Analysis and Measure Theory.- 4. Some Results from Ergodic Theory.- 5. Some Background in Complex Analysis.- 6. Some Results from Functional Analysis.
£104.49
Aarhus University Press Stochastic Dynamics
Book SynopsisIn chapter 1, the basic assumptions of the random vibration theory are emphasized. In chapters 2 and 3, pertinent results of stochastic variables and stochastic processes have been indicated. Chapter 4 deals with the stochastic response analysis of single degrees-of-freedom, multi-degrees-of-freedom and continuous linear structural systems. In principle, an introductory course on linear structural dynamics is presupposes. However, in order to make this textbook self-contained, short reviews of the most important results of linear deterministic vibration theory have been included in the start of the relevant sub-sections. Chapter 5 outlines the reliability theory for dynamically excited building structures, i.e., reliability theory for narrowbanded response processes. Finally, Chapter 6 gives an introduction to Monte Carlo simulation methods, which become increasingly important and useful as the computers become more and more powerful.
£18.95
Birkhauser Verlag AG Topics in stochastic processes
Book SynopsisThe notes are based on lectures on stochastic processes given at Scuola Normale Superiore in 1999 and 2000. Some new material was added and only selected, less standard results were presented. We did not include several applications to statistical mechanics and mathematical finance, covered in the lectures, as we hope to write part two of the notes devoted to applications of stochastic processes in modelling. The main themes of the notes are constructions of stochastic processes. We present different approaches to the existence question proposed by Kolmogorov, Wiener, Ito and Prohorov. Special attention is also paid to Levy processes. The lectures are basically self-contained and rely only on elementary measure theory and functional analysis. They might be used for more advanced courses on stochastic processes.
£18.04
Birkhauser Verlag AG Probabilistic methods of investigating interior
Book SynopsisThe lectures concentrate on some old and new relations between quasiderivatives of solutions to Ito stochastic equations and interior smoothness of harmonic functions associated with degenerate elliptic equations. Recent progress in the case of constant coefficients is discussed in full detail.
£11.99
Birkhauser Verlag AG Probability, Uncertainty and Rationality
Book SynopsisThis volume explores, from a mathematical and a philosophical perspective, the virtuous circle connecting logic and rationality. While logic lends its methods, techniques and ideas to the investigation of rationality, the practical problems which arise in modelling rational behaviour, especially in the social sciences, motivate logicians to develop more refined logical formalisms. This is why non classical logics - a unifying theme of this volume - play a fundamental role in the construction of formal models of rationality.Table of ContentsIntroduction.- 1. Foundations.- Ordered algebras and logic. George Metcalfe, Francesco Paoli and Constantine Tsinakis.- 2. Probability. The social entropy process: Axiomatising the aggregation of probabilistic beliefs. George Wilmers.- Conditional probability in the light of qualitative belief change. David Makinson.- Is there a probability theory of many-valued events? Vincenzo Marra.- 3. Uncertainty.- On Giles style dialogue games and hypersequent systems. Christian G. Fermüller.- Poset representation for free RDP-algebras. Diego Valota.- Uncertainty, indeterminacy and fuzziness: A probabilistic approach. Martina Fedel.- 4. Rationality.- Tractable depth-bounded logics and the problem of logical omniscience. Marcello D’Agostino.- Rational behaviour at trust nodes. Hykel Hosni and Silvia Milano.
£25.64
Springer Verlag, Singapore Elementary Statistical Methods
Book SynopsisThis is the first book of two volumes covering the basics of statistical methods and analysis. Significant topics include concepts of research and data analysis, descriptive statistics, probability and distributions, correlation and regression, and statistical inference. The book includes useful examples and exercises as well as relevant case studies for proper implementation of the discussed tools. This book will be a valuable text for undergraduate students of statistics, management, economics, and psychology, wanting to gain basic understanding of statistics and the usage of its various concepts. Table of Contents1. Concepts in Research and Data Analysis.- 2. Descriptive Statistics.- 3. Probability and Distributions.- 4. Correlation and Regression.- 5. Statistical Inference.
£94.99
Springer Verlag, Singapore An Introduction to Stochastic Thermodynamics: From Basic to Advanced
Book SynopsisThis book presents the fundamentals of stochastic thermodynamics, one of the most central subjects in non-equilibrium statistical mechanics. It also explores many recent advances, e.g., in information thermodynamics, the thermodynamic uncertainty relation, and the trade-off relation between efficiency and power. The content is divided into three main parts, the first of which introduces readers to fundamental topics in stochastic thermodynamics, e.g., the basics of stochastic processes, the fluctuation theorem and its variants, information thermodynamics, and large deviation theory. In turn, parts two and three explore advanced topics such as autonomous engines (engines not controlled externally) and finite speed engines, while also explaining the key concepts from recent stochastic thermodynamics theory that are involved. To fully benefit from the book, readers only need an undergraduate-level background in statistical mechanics and quantum mechanics; no background in information theory or stochastic processes is needed. Accordingly, the book offers a valuable resource for early graduate or higher-level readers who are unfamiliar with this subject but want to keep up with the cutting-edge research in this field. In addition, the author’s vivid descriptions interspersed throughout the book will help readers grasp ‘living’ research developments and begin their own research in this field.Table of Contents
£98.99
Springer Verlag, Singapore Stochastic Volatility and Realized Stochastic
Book SynopsisThis treatise delves into the latest advancements in stochastic volatility models, highlighting the utilization of Markov chain Monte Carlo simulations for estimating model parameters and forecasting the volatility and quantiles of financial asset returns. The modeling of financial time series volatility constitutes a crucial aspect of finance, as it plays a vital role in predicting return distributions and managing risks. Among the various econometric models available, the stochastic volatility model has been a popular choice, particularly in comparison to other models, such as GARCH models, as it has demonstrated superior performance in previous empirical studies in terms of fit, forecasting volatility, and evaluating tail risk measures such as Value-at-Risk and Expected Shortfall. The book also explores an extension of the basic stochastic volatility model, incorporating a skewed return error distribution and a realized volatility measurement equation. The concept of realized volatility, a newly established estimator of volatility using intraday returns data, is introduced, and a comprehensive description of the resulting realized stochastic volatility model is provided. The text contains a thorough explanation of several efficient sampling algorithms for latent log volatilities, as well as an illustration of parameter estimation and volatility prediction through empirical studies utilizing various asset return data, including the yen/US dollar exchange rate, the Dow Jones Industrial Average, and the Nikkei 225 stock index. This publication is highly recommended for readers with an interest in the latest developments in stochastic volatility models and realized stochastic volatility models, particularly in regards to financial risk management.Table of Contents1 Introduction.- 2 Stochastic Volatility Model.- 3 Asymmetric Stochastic Volatility Model.- 4 Stochastic Volatility Model with Generalized Hyperbolic Skew Student’s t Error.- 5 Realized Stochastic Volatility Model.
£39.99
Springer Verlag, Singapore Applied Linear Algebra, Probability and
Book SynopsisThis book focuses on research in linear algebra, statistics, matrices, graphs and their applications. Many chapters in the book feature new findings due to applications of matrix and graph methods. The book also discusses rediscoveries of the subject by using new methods. Dedicated to Prof. Calyampudi Radhakrishna Rao (C.R. Rao) who has completed 100 years of legendary life and continues to inspire us all and Prof. Arbind K. Lal who has sadly departed us too early, it has contributions from collaborators, students, colleagues and admirers of Professors Rao and Lal. With many chapters on generalized inverses, matrix analysis, matrices and graphs, applied probability and statistics, and the history of ancient mathematics, this book offers a diverse array of mathematical results, techniques and applications. The book promises to be especially rewarding for readers with an interest in the focus areas of applied linear algebra, probability and statistics.Table of ContentsChapter 1. On Some Matrix Versions of Covariance, Harmonic Mean and other Inequalities: An Overview.- Chapter 2. The Impact of Professor C. R. Rao's Research used in solving problems in Applied Probability.- Chapter 3. Upper ounds for the Euclidean distances between the BLUEs under the partitioned linear fixed model and the corresponding mixed model.- Chapter 4. Nucleolus Computation for some Structured TU Games via Graph Theory and Linear Algebra.- Chapter 5. From Linear System of Equations to Artificial Intelligence - The evolution Journey of Computer Tomographic Image Reconstruction Algorithms.- Chapter 6. Shapley Value and other Axiomatic Extensions to Shapley Value.- Chapter 7. An Accelerated Block Randomized Kaczmarz Methos.- Chapter 8. Nullity of Graphs - A Survey and Some New Results.- Chapter 9. Some Observations on Algebraic Connectivity of Graphs.- Chapter 10. Orthogonality for iadjoints f Operators.- Chapter 11. Permissible covariance structures for simultaneous retention of BLUEs in small and big linear models.- Chapter 12. On some Special Matrices and its Applications in Linear Complementarity Problem.- Chapter 3. On Nearest Matrix with Partially Specified Eigen Structure.- Chapter 14. Equality of BLUEs for Full, Small, and Intermediate Linear Models under Covariance Change, with links to Data Confidentiality and Encryption.-Chapter 15. Statistical Inference for Middle Censored Data with Applications. etc
£113.99
Elsevier Science A Course in Probability Theory
Book SynopsisThis book is designed for undergraduate programs and students and can also be used as a first-year graduate text in probability. It offers a broad perspective, building on the synopsis of measure and integration offered in Chapter two.
£65.54
Taylor & Francis Ltd Designing Engineering Structures using Stochastic Optimization Methods
a huge range and FREE tracked UK delivery on ALL orders.
£58.89
Taylor & Francis Ltd Discrete Stochastic Models and Applications for Reliability Engineering and Statistical Quality Control
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£128.25
Taylor & Francis Art of Smooth Pasting
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£285.00
Taylor & Francis Routledge Companion to Intelligence Studies
a huge range and FREE tracked UK delivery on ALL orders.
£209.00
