Understanding Markov Chains

Examples and Applications

  • Nicolas┬áPrivault
Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Nicolas Privault
    Pages 1-6
  3. Nicolas Privault
    Pages 7-36
  4. Nicolas Privault
    Pages 37-60
  5. Nicolas Privault
    Pages 61-75
  6. Nicolas Privault
    Pages 77-94
  7. Nicolas Privault
    Pages 95-116
  8. Nicolas Privault
    Pages 117-128
  9. Nicolas Privault
    Pages 129-148
  10. Nicolas Privault
    Pages 149-166
  11. Nicolas Privault
    Pages 167-209
  12. Nicolas Privault
    Pages 211-223
  13. Nicolas Privault
    Pages 225-239
  14. Nicolas Privault
    Pages 241-245
  15. Back Matter
    Pages 247-354

About this book

Introduction

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.

Keywords

Applications of Stochastic Processes Discrete and continuous-time Markov Chains First-step analysis in Markov Chains Gambling Processes and random walks in Markov Chains Highly accessible textbook on Stochastic Processes Introduction to Stochastic Processes Markov Chains self-study Markov Chains textbook Markov Chains textbook with examples Modern textbook on Stochastic Processes Nicolas Privault Stochastic Processes Solved problems in Markov Chains

Authors and affiliations

  • Nicolas┬áPrivault
    • 1
  1. 1.School of Physical and Mathematical SciencesNanyang Technological UniversitySingaporeSingapore

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-4451-51-2
  • Copyright Information Springer Science+Business Media Singapore 2013
  • Publisher Name Springer, Singapore
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-981-4451-50-5
  • Online ISBN 978-981-4451-51-2
  • Series Print ISSN 1615-2085
  • About this book