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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.
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.
| Erscheinungsjahr: | 2026 |
|---|---|
| Fachbereich: | Wahrscheinlichkeitstheorie |
| Genre: | Importe, Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Springer Undergraduate Mathematics Series |
| Inhalt: |
xix
366 S. 12 s/w Illustr. 106 farbige Illustr. 366 p. 118 illus. 106 illus. in color. |
| ISBN-13: | 9789819540563 |
| ISBN-10: | 9819540569 |
| Sprache: | Englisch |
| Herstellernummer: | 978-981-95-4056-3 |
| Einband: | Kartoniert / Broschiert |
| Autor: | Privault, Nicolas |
| Auflage: | Third Edition 2026 |
| Hersteller: |
Springer Singapore
Springer-Verlag GmbH |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Abbildungen: | XIX, 366 p. 118 illus., 106 illus. in color. |
| Maße: | 18 x 155 x 235 mm |
| Von/Mit: | Nicolas Privault |
| Erscheinungsdatum: | 28.05.2026 |
| Gewicht: | 0,657 kg |
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