Understanding Markov chains examples and applications Nicolas Privault

Format:

Book

Author/Creator:

Privault, Nicolas, author.

Series:

Springer undergraduate mathematics series

Language:

English

Subjects (All):

Markov processes.

Physical Description:

1 online resource

Place of Publication:

Singapore Springer 2013

Language Note:

English

System Details:

text file

PDF

Summary:

This book provides an undergraduate introduction to discrete andcontinuous-time Markov chains and their applications. A large focus is placed on the first step analysistechnique and its applications to average hitting times and ruin probabilities. Classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes, are also covered. Two major examples (gambling processes and random walks) are treated in detail from the beginning, before the general theory itself is presented in the subsequent chapters. An introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times is also provided, and the book includes a chapter on spatial Poisson processes with some recent results on moment identities and deviation inequalities for Poisson stochastic integrals. The concepts presented are illustrated by examples and by 72 exercises and their complete solutions

Contents:

Introduction Probability Background Gambling Problems Random Walks Discrete-Time Markov Chains First Step Analysis Classification of States Long-Run Behavior of Markov Chains Branching Processes Continuous-Time Markov Chains Discrete-Time Martingales Spatial Poisson Processes Reliability Theory

Notes:

Includes bibliographical references and index

Print version record

Other Format:

Print version Privault, Nicolas. Understanding Markov chains

ISBN:

9789814451512

9814451517

OCLC:

857281878

Access Restriction:

Restricted for use by site license