Markov Processes

James R. Kirkwood (Sweet Briar College, Virginia, USA)

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English

CRC Press
28 October 2025

Probability & statistics; Stochastics

Series: Advances in Applied Mathematics

Markov Processes provides a bridge from an undergraduate probability course to a course in stochastic processes. The text is designed to be understandable to students who have taken an undergraduate probability course without needing an instructor to fill in any gaps.

Clear, rigorous, and intuitive, the second edition builds on the successful first, used in courses and as a reference for those who want to see detailed proofs of the theorems of Markov processes. It contains copious computational examples that motivate and illustrate the theorems.

This second edition presents a new chapter illustrating the utility of using digraphs to describe whether a Markov process is reducible, absorbing, etc. There are additional exercises, and some material has been applied in a number of fields, including economics, physics, and mathematical biology.

This book begins with a review of basic probability, then covers the case of finite-state, discrete-time Markov processes. Building on this, the text deals with the discrete-time, infinite-state case and provides background for continuous Markov processes with exponential random variables and Poisson processes. It presents continuous Markov processes that include the basic content of Kolmogorov’s equations, infinitesimal generators, and explosions. This book concludes with coverage of both discrete and continuous reversible Markov chains.

While Markov processes are touched on in probability courses, this book offers the opportunity to concentrate on the topic when additional study is required. It creates a more seamless transition to prepare the student for what comes next.

By: James R. Kirkwood (Sweet Briar College Virginia USA)
Imprint: CRC Press
Country of Publication: United Kingdom
Edition: 2nd edition
Dimensions: Height: 234mm, Width: 156mm,
Weight: 640g
ISBN: 9781041046660
ISBN 10: 1041046669
Series: Advances in Applied Mathematics
Pages: 337
Publication Date: 28 October 2025
Audience: College/higher education , A / AS level
Format: Paperback
Publisher's Status: Forthcoming

Preface to Second Edition 1. Review of Probability 2. Discrete-Time, Finite-State Markov Chains 3. Discrete-Time, Infinite-State Markov Chains 4. Exponential Distribution and Poisson Process 5. Continuous Time Markov Chains 6. Queuing Models and Detailed Balance Equations 7. Reversible Markov Chains 8.Digraphs

James R. Kirkwood holds a Ph.D. from the University of Virginia. He has had ten mathematics textbooks published on various topics including calculus, real analysis, mathematical biology and mathematical physics. His original research was in mathematical physics, and he co-authored the seminal paper in a topic now called Kirkwood-Thomas Theory in mathematical physics. During the summer, he teaches real analysis to graduate students at the University of Virginia. He has been awarded several National Science Foundation grants. Dr. Kirkwood’s books for CRC Press include, An Introduction to Analysis, third edition ©2024; A Transition to Advanced Mathematics (with Raina S. Robeva) ©2024; Linear Algebra (with Bessie H. Kirkwood) ©2024; Elementary Linear Algebra (with Bessie H. Kirkwood) ©2023.