Markov processes /

Kirkwood, the author of An Introduction to Analysis (2nd ed., 2002) and Mathematical Physics with Partial Differential Equations (2013), has published another significant mathematics monograph. Markov Processes consists of reviews of probability, discrete Markov chains, continuous Markov chains, and time-reversible Markov chains. The section on discrete Markov chains presents the fundamental concepts of discrete finite-state and infinite-state processes such as absorbing states, periodicity, reducibility, transient renewal processes, and branch processes. The components of continuous Markov chains span exponential distribution and Poisson processes, Kolmogorov forward and backward equations, M/M/s type queuing models, and birth-death processes. Readers need a mathematical background in calculus-based probability theory and linear algebra to follow the text. It is suitable for audiences who strive to grasp the fundamental concepts of various types of Markov processes or to prepare for learning advanced stochastic processes. The monograph can serve as a textbook since it provides essential examples and exercise problems applied in economics, finance, engineering, physics, and biology. However, the inclusion of computational examples based on programming tools such as MATLAB and R would have enhanced the book's usability. Summing Up: Recommended. Upper-division undergraduates through professionals/practitioners. --Seong-Tae Kim, North Carolina A&T State University