Springer Undergraduate Mathematics Series: Understanding Markov Chains (PDF)
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This book provides an undergraduate introduction to discrete and continuous-time Markov chains and their applications. A large focus is placed on the first step analysis technique and its applications to average hitting times and ruin probabilities. Classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes, are also covered. Two major examples (gambling processes and random walks) are treated in detail from the beginning, before the general theory itself is presented in the subsequent chapters.
An introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times is also provided, and the book includes a chapter on spatial Poisson processes with some recent results on moment identities and deviation inequalities for Poisson stochastic integrals. The concepts presented are illustrated by examples and by 72 exercises and their complete solutions.
- Autor: Nicolas Privault
- 2013, Englisch
- Verlag: Springer Singapore
- ISBN-10: 9814451517
- ISBN-13: 9789814451512
- Erscheinungsdatum: 13.08.2013
Abhängig von Bildschirmgröße und eingestellter Schriftgröße kann die Seitenzahl auf Ihrem Lesegerät variieren.
- Dateiformat: PDF
- Größe: 3.61 MB
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“The book provides an introduction to discrete and continuous-time Markov chains and their applications. … The explanation is detailed and clear. Often the reader is guided through the less trivial concepts by means of appropriate examples and additional comments, including diagrams and graphs. Also, a big plus is the presence of numerous well-chosen exercises at the end of each chapter, which are discussed in a separate ‘Solutions to the Exercises’ part at the end of the book.” (Michele Zito, Mathematical Reviews, December, 2014)
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