Understanding Markov chains : examples and applications /

Understanding Markov chains : examples and applications /

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Bibliographic Details
Author / Creator:	Privault, Nicolas, author.
Imprint:	Singapore : Springer, 2013.
Description:	1 online resource.
Language:	English
Series:	Springer undergraduate mathematics series Springer undergraduate mathematics series.
Subject:	Markov processes. Markov processes.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/9852337

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ISBN:	9789814451512 (electronic bk.) 9814451517 (electronic bk.) 9789814451505 9814451509
Notes:	Includes bibliographical references and index. Description based on print version record.
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.
Other form:	Print version: Privault, Nicolas, author. Understanding Markov chains 9789814451505
Standard no.:	10.1007/978-981-4451-51-2

Table of 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.