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Understanding Markov chains : examples and applications / Nicolas Privault.

By: Material type: TextTextSeries: Springer undergraduate mathematics seriesPublisher: Singapore : Springer, [2013]Copyright date: ©2013Description: ix, 354 pages : illustrations ; 24 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 9814451509
  • 9789814451505
Subject(s): Additional physical formats: No titleDDC classification:
  • 519.233 23
LOC classification:
  • QA274.7 .P76 2013
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 -- Some useful identities -- Solutions to the exercises -- Bibliography -- Index.
Summary: "This book provides an undergraduate introduction to discrete and continuous-time Markov chains and their applications. A large focus is placed on the first step analysis technique 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." --Publisher's website.
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Holdings
Item type Current library Call number Copy number Status Date due Barcode
Book City Campus City Campus Main Collection 519.233 PRI (Browse shelf(Opens below)) 1 Available A555257B

Includes bibliographical references and index.

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 -- Some useful identities -- Solutions to the exercises -- Bibliography -- Index.

"This book provides an undergraduate introduction to discrete and continuous-time Markov chains and their applications. A large focus is placed on the first step analysis technique 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." --Publisher's website.

Machine converted from AACR2 source record.

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