Understanding Markov Chains: Examples and Applications (Springer Undergraduate Mathematics Series) - Softcover

Privault, Nicolas

Softcover

ISBN 10: 9819540569 ISBN 13: 9789819540563

Publisher: Springer, 2026

Synopsis

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 the computation of 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 starts by examining in detail two important examples (gambling processes and random walks) before presenting the general theory 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, 150 exercises and 22 problems with their solutions.

This book is a revised and expanded version of the previous edition, and includes additional exercises and problems with complete solutions. As in the previous book, all exercises and problems are solved in detail, with many graphs and explanatory figures.

About this title

About the Author

The author is a 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 books, Stochastic Analysis in Discrete and Continuous Settings: With Normal Martingales, Lecture Notes in Mathematics, Springer, 2009, and Discrete Stochastic Processes - Tools for Machine Learning and Data Science, Springer Undergraduate Mathematics Series 2024, and was a co-editor for the book, Stochastic Analysis with Financial Applications, Progress in Probability, Vol. 65, Springer Basel, 2011. Aside from these four Springer titles, he has authored several others. The manuscript has been developed over the years from his courses on Stochastic Processes at NTU.

From the Back Cover

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 the computation of 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 starts by examining in detail two important examples (gambling processes and random walks) before presenting the general theory 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, 150 exercises and 22 problems with their solutions.

This book is a revised and expanded version of the previous edition, and includes additional exercises and problems with complete solutions. As in the previous book, all exercises and problems are solved in detail, with many graphs and explanatory figures.

Edition details

• Publisher: Springer
• Publication date: 2026
• Language: English
• ISBN 10: 9819540569
• ISBN 13: 9789819540563
• Binding: Paperback
• Edition number: 3
• Number of pages: 385