© 2018

Understanding Markov Chains

Examples and Applications


  • Easily accessible to both mathematics and non-mathematics majors who are taking an introductory course on Stochastic Processes

  • Filled with numerous exercises to test students' understanding of key concepts

  • A gentle introduction to help students ease into later chapters, also suitable for self-study

  • Accompanied with computer simulation codes in R and Python


Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Nicolas Privault
    Pages 1-37
  3. Nicolas Privault
    Pages 39-67
  4. Nicolas Privault
    Pages 69-87
  5. Nicolas Privault
    Pages 89-113
  6. Nicolas Privault
    Pages 115-145
  7. Nicolas Privault
    Pages 147-162
  8. Nicolas Privault
    Pages 163-188
  9. Nicolas Privault
    Pages 189-209
  10. Nicolas Privault
    Pages 211-262
  11. Nicolas Privault
    Pages 263-280
  12. Nicolas Privault
    Pages 281-288
  13. Nicolas Privault
    Pages 289-293
  14. Back Matter
    Pages 295-372

About this book


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.


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

  1. 1.School of Physical and Mathematical SciencesNanyang Technological UniversitySingaporeSingapore

About the authors

The author is an associate professor from the Nanyang Technological University (NTU) and is well-established in the field of stochastic processes and a highly respected probabilist. He has authored the book, Stochastic Analysis in Discrete and Continuous Settings: With Normal Martingales, Lecture Notes in Mathematics, Springer, 2009 and was a co-editor for the book, Stochastic Analysis with Financial Applications, Progress in Probability, Vol. 65, Springer Basel, 2011. Aside from these two Springer titles, he has authored several others. He is currently teaching the course M27004-Probability Theory and Stochastic Processes at NTU. The manuscript has been developed over the years from his courses on Stochastic Processes.

Bibliographic information

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