Markov Chains

Author: J. R. Norris

Publisher: Cambridge University Press

ISBN: 1107393477

Category: Mathematics

Page: N.A

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Markov chains are central to the understanding of random processes. This is not only because they pervade the applications of random processes, but also because one can calculate explicitly many quantities of interest. This textbook, aimed at advanced undergraduate or MSc students with some background in basic probability theory, focuses on Markov chains and quickly develops a coherent and rigorous theory whilst showing also how actually to apply it. Both discrete-time and continuous-time chains are studied. A distinguishing feature is an introduction to more advanced topics such as martingales and potentials in the established context of Markov chains. There are applications to simulation, economics, optimal control, genetics, queues and many other topics, and exercises and examples drawn both from theory and practice. It will therefore be an ideal text either for elementary courses on random processes or those that are more oriented towards applications.
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Introduction to Markov Chains

With Special Emphasis on Rapid Mixing

Author: Ehrhard Behrends

Publisher: Vieweg+Teubner Verlag

ISBN: 3322901572

Category: Mathematics

Page: 234

View: 4321

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Besides the investigation of general chains the book contains chapters which are concerned with eigenvalue techniques, conductance, stopping times, the strong Markov property, couplings, strong uniform times, Markov chains on arbitrary finite groups (including a crash-course in harmonic analysis), random generation and counting, Markov random fields, Gibbs fields, the Metropolis sampler, and simulated annealing. With 170 exercises.
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Understanding Markov Chains

Examples and Applications

Author: Nicolas Privault

Publisher: Springer

ISBN: 9811306591

Category: Mathematics

Page: 372

View: 5079

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This book provides an undergraduate-level introduction to discrete and continuous-time Markov chains and their applications, with a particular focus on the first step analysis technique and its applications to average hitting times and ruin probabilities. It also discusses classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes. It first examines in detail two important examples (gambling processes and random walks) before presenting the general theory itself in the subsequent chapters. It also provides an introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times, together with a chapter on spatial Poisson processes. The concepts presented are illustrated by examples, 138 exercises and 9 problems with their solutions.
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Markov Chains and Mixing Times: Second Edition

Author: David A. Levin,Yuval Peres

Publisher: American Mathematical Soc.

ISBN: 1470429624

Category: Distribution (Probability theory)

Page: 447

View: 9057

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This book is an introduction to the modern theory of Markov chains, whose goal is to determine the rate of convergence to the stationary distribution, as a function of state space size and geometry. This topic has important connections to combinatorics, statistical physics, and theoretical computer science. Many of the techniques presented originate in these disciplines. The central tools for estimating convergence times, including coupling, strong stationary times, and spectral methods, are developed. The authors discuss many examples, including card shuffling and the Ising model, from statistical mechanics, and present the connection of random walks to electrical networks and apply it to estimate hitting and cover times. The first edition has been used in courses in mathematics and computer science departments of numerous universities. The second edition features three new chapters (on monotone chains, the exclusion process, and stationary times) and also includes smaller additions and corrections throughout. Updated notes at the end of each chapter inform the reader of recent research developments.
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Formal Methods for Components and Objects

Third International Symposium, FMCO 2004, Leiden, The Netherlands, November 2-5, 2004, Revised Lectures

Author: Frank S. de Boer,Marcello M. Bonsangue,Susanne Graf,Willem-Paul de Roever

Publisher: Springer

ISBN: N.A

Category: Formal methods (Computer science)

Page: 325

View: 7736

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Formal methods have been applied successfully to the verification of medium-sized programs in protocol and hardware design. However, their application to the development of large systems requires more emphasis on specification, modelling and validation techniques supporting the concepts of reusability and modifiability, and their implementation in new extensions of existing programming languages. This book presents revised tutorial lectures given by invited speakers at the Third International Symposium on Formal Methods for Components and Objects, FMCO 2004, held in Leiden, The Netherlands, in November 2004. The 14 revised lectures by leading researchers present a comprehensive account of the potential of formal methods applied to large and complex software systems such as component-based systems and object systems. The book provides an unique combination of ideas on software engineering and formal methods that reflect the expanding body of knowledge on modern software systems.
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Statistical Analysis of Stochastic Processes in Time

Author: J. K. Lindsey

Publisher: Cambridge University Press

ISBN: 9781139454513

Category: Mathematics

Page: 338

View: 1682

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This book was first published in 2004. Many observed phenomena, from the changing health of a patient to values on the stock market, are characterised by quantities that vary over time: stochastic processes are designed to study them. This book introduces practical methods of applying stochastic processes to an audience knowledgeable only in basic statistics. It covers almost all aspects of the subject and presents the theory in an easily accessible form that is highlighted by application to many examples. These examples arise from dozens of areas, from sociology through medicine to engineering. Complementing these are exercise sets making the book suited for introductory courses in stochastic processes. Software (available from www.cambridge.org) is provided for the freely available R system for the reader to apply to all the models presented.
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An Introduction to Stochastic Processes with Applications to Biology

Author: Linda J. S. Allen

Publisher: Prentice Hall

ISBN: 9780130352187

Category: Mathematics

Page: 385

View: 2671

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Plenty of examples, diagrams, and figures take readers step-by-step through well-known classical biological models to ensure complete understanding of stochastic formulation. Probability, Markov Chains, discrete time branching processes, population genetics, and birth and death chains. For biologists and other professionals who want a comprehensive, easy-to-follow introduction to stochastic formulation as it pertains to biology.
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Statistical Models

Author: A. C. Davison

Publisher: Cambridge University Press

ISBN: 1139437410

Category: Mathematics

Page: N.A

View: 6176

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Models and likelihood are the backbone of modern statistics. This 2003 book gives an integrated development of these topics that blends theory and practice, intended for advanced undergraduate and graduate students, researchers and practitioners. Its breadth is unrivaled, with sections on survival analysis, missing data, Markov chains, Markov random fields, point processes, graphical models, simulation and Markov chain Monte Carlo, estimating functions, asymptotic approximations, local likelihood and spline regressions as well as on more standard topics such as likelihood and linear and generalized linear models. Each chapter contains a wide range of problems and exercises. Practicals in the S language designed to build computing and data analysis skills, and a library of data sets to accompany the book, are available over the Web.
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Probability

Theory and Examples

Author: Rick Durrett

Publisher: Cambridge University Press

ISBN: 113949113X

Category: Mathematics

Page: N.A

View: 4222

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This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.
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