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A First Look at Stochastic Processes
Rosenthal J., WORLD SCIENTIFIC, Singapore, 2020. 202 pp. Type: Book (978-9-811208-97-3)
Date Reviewed: Jul 1 2022

Although intended as a textbook, Rosenthal’s A first look at stochastic processes is not quite there. However, it is still a very interesting and useful text with a good account of challenging problems. While the author has done well to provide in-depth coverage of Markov chains and martingales, other topics such as stationarity, branching processes, renewal processes, Brownian motion, Poisson processes, Gaussian Processes, and so on could have been dealt with more seriously, as one would expect in a textbook, rather than in examples.

On the application side, the author lucidly addresses well-known topics such as Markov chain Monte Carlo (MCMC), stock option pricing, the gambler’s ruin problem, random walk, queueing theory, and so on, but again all of these topics have an extensive literature and demand a separate chapter or subchapter in a textbook rather than to be discussed only as examples.

On the plus side, the author’s explanations of the basic theorems in a friendly yet logical style is praiseworthy. I found the examples of waiting for a bus, the jumping frog, and repeated gambling, to name a few, quite absorbing.

On the negative side, apart from what I stated earlier, a thorough discussion on Akaike’s information criterion (AIC) for determining the order of Markov chains and the important fact that sometimes a deterministic response can also be profitably realized as the outcome of a stochastic process (as in a computer experiment, for example, to achieve cheap and efficient prediction) were found wanting.

In summary, I found it more of a motivational book for learning more about stochastic processes from standard texts on the topic (see, for example, Gallager [1]). Nevertheless, considering the wealth of solved problems and easy presentation of the fundamental concepts, it is a welcome addition to the existing literature. Applied mathematical and computing scientists, advanced undergraduate students, and practitioners should find it to be a helpful reference book.

The prerequisite for understanding this book is a sound knowledge of applied probability theory, linear algebra, and advanced calculus.

Reviewer:  Soubhik Chakraborty Review #: CR147464 (2208-0107)
1) Gallager, R. G. Stochastic processes: theory for applications. Cambridge University Press, New York, NY, 2013.
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