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Modeling, Analysis, Design, and Control of Stochastic Systems (Springer Texts in Statistics) Hardcover – December 15, 2000
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From the reviews of the second edition:
“The author has added a new chapter on Poisson processes and another one on Brownian motion. The discussion is kept on an elementary level and does not require any knowledge from measure theory or advanced calculus. … the text is suitable for an undergraduate course on probabilistic modeling for students from physics, engineering, operations research, computer science, business administration or some related field that needs advanced modeling techniques.” (H. M. Mai, Zentralblatt MATH, Vol. 1222, 2011)
“Suitable for undergraduates in Mathematics, Statistics, Operations Research, Computer Science, Business Administration, Public Policy, etc. This is a very clear and readable text on Markov chains, Poisson processes, continuous time Markov chains, renewal processes, and queuing processes. … The treatment is very clear, intuitive as well as rigorous, without being pedantic, and full of interesting examples and case studies. … The book should be fun to teach from and learn from.” (Jayanta K. Ghosh, International Statistical Review, Vol. 80 (3), 2012)--This text refers to the Paperback edition.
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Grad students will find probably find it useful too, since after the review, discrete and continuous Markov chains, queuing models and other topics are presented and illustrated with many examples. They serve to clarify propositions and theorems that are formally proved.
In general, I think this book helps to develop the intuition necessary to use Markov processes in many practical applications, and understand higher level texts.
Of course, having a broad topic coverage at introductory level, some more advenced topics (like positive and null recurrency) had to be left out, so grad students will need some other reference too (Kulkarni has a grad text, in case you like this one).
However, if you are a novice trying to learn about stochastics and want good explanations and examples with an appropriate buildup, I would not recommend the book.
As an example, the review discussion of probability in the first four chapters didn't even come close to comparing with the probability book I used in another class. If you are near a bookstore, you can easily verify this. I imagine that this comparison (or lack thereof) would hold for many other probability textbooks. Also, if presentation makes a difference to you, this is quite minimalist.
Another area that I found lacking is that the answers in the back just provide a numerical answer without any explanation to how solutions were arrived at. While this is often the case for other books, the author did not provide a sufficient base for a novice to work the problems. As a result, most of the end of chapter problems were of little use in helping me better learn the materials. A good workbook or better explanations would be very helpful.
While there are certainly couple areas that I found worthwhile and this does appear to be one of the only books on this niche area (the lack of competition may explain a lot of why the shortcomings exist and why this doesn't have the feel of real textbook), this first edition book needs some serious work to make it truly effective and user friendly.