Overview
- 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
- Request lecturer material: sn.pub/lecturer-material
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
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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.
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Keywords
- 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
Table of contents (12 chapters)
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Front Matter
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Back Matter
Authors and Affiliations
About the author
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
Book Title: Understanding Markov Chains
Book Subtitle: Examples and Applications
Authors: Nicolas Privault
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-981-13-0659-4
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2018
Softcover ISBN: 978-981-13-0658-7Published: 15 August 2018
eBook ISBN: 978-981-13-0659-4Published: 03 August 2018
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 2
Number of Pages: XVII, 372
Number of Illustrations: 44 b/w illustrations
Topics: Probability Theory and Stochastic Processes, Statistical Theory and Methods, Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences