Understanding Markov Chains
Description
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.
Reviews / Votes
"This textbook provides an elementary introduction to the classical theory of discrete and continuous time Markov chains motivated by gambling problems and covers a variety of primers on different topics . . this text may serve very well for a first undergraduate course on Markov chains for applied mathematicians, but also for students of financial engineering. It is completed by almost a hundred pages of solutions of exercises." (Michael Högele, zbMATH 1305.60003, 2015)
"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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