Understanding Markov Chains
Examples and Applications
Authors: Privault, Nicolas
Free Preview- 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
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- About this Textbook
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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 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.
- About the authors
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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.
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- Table of contents (12 chapters)
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Probability Background
Pages 1-37
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Gambling Problems
Pages 39-67
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Random Walks
Pages 69-87
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Discrete-Time Markov Chains
Pages 89-113
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First Step Analysis
Pages 115-145
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Table of contents (12 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Understanding Markov Chains
- Book Subtitle
- Examples and Applications
- Authors
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- Nicolas Privault
- Series Title
- Springer Undergraduate Mathematics Series
- Copyright
- 2018
- Publisher
- Springer Singapore
- Copyright Holder
- Springer Nature Singapore Pte Ltd.
- eBook ISBN
- 978-981-13-0659-4
- DOI
- 10.1007/978-981-13-0659-4
- Softcover ISBN
- 978-981-13-0658-7
- Series ISSN
- 1615-2085
- Edition Number
- 2
- Number of Pages
- XVII, 372
- Number of Illustrations
- 44 b/w illustrations
- Topics
