Understanding Markov Chains

Examples and Applications

Nicolas Privault (Autor)

Buch | Softcover

364 Seiten

2026 | Third Edition 2026
Springer Verlag, Singapore
978-981-95-4056-3 (ISBN)

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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.

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.

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.

Erscheinungsdatum	29.11.2025
Reihe/Serie	Springer Undergraduate Mathematics Series
Zusatzinfo	92 Illustrations, color; 4 Illustrations, black and white
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	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
ISBN-10	981-95-4056-9 / 9819540569
ISBN-13	978-981-95-4056-3 / 9789819540563
Zustand	Neuware