- Series: Cambridge Series in Statistical and Probabilistic Mathematics (Book 2)
- Paperback: 254 pages
- Publisher: Cambridge University Press (July 28, 1998)
- Language: English
- ISBN-10: 0521633966
- ISBN-13: 978-0521633963
- Product Dimensions: 7 x 0.6 x 10 inches
- Shipping Weight: 1.2 pounds (View shipping rates and policies)
- Average Customer Review: 3.3 out of 5 stars See all reviews (13 customer reviews)
- Amazon Best Sellers Rank: #1,044,657 in Books (See Top 100 in Books)
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Markov Chains (Cambridge Series in Statistical and Probabilistic Mathematics)
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"...impressive ....I heartily recommend this book....this is the best book available summarizing the theory of Markov Chains....Norris achieves for Markov Chains what Kingman has so elegantly achieved for Poisson processes....Such creative tinkering will be a pleasure to many teachers." Bulletin of Mathematical Biology
Markov chains are central to the understanding of random processes. This textbook, aimed at advanced undergraduate or MSc students with some background in basic probability theory, focuses on Markov chains and develops quickly a coherent and rigorous theory whilst showing also how actually to apply it. There are applications to simulation, economics, optimal control, genetics, queues and many other topics, and a careful selection of exercises and examples drawn both from theory and practice.
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Top Customer Reviews
My only complaint in the first half of the text regards the definition of continuous time Markov chains. The definition is introduced using the technical concepts of jump chain/holding time properties. This doesn't tie out well with the treatment of the discrete time case and may seem counter-intuitive to readers initially. However, the author does establish the equivalence of the jump chain/holding time definition to the usual transition probability definition towards the end of Chapter 2.
The second half of the text deals with the relationship of Markov chains to other aspects of stochastic analysis and the application of Markov chains to applied settings.
In Chapter 4, the material takes a serious jump (explosion?) in sophistication level. In this chapter, the author introduces filtrations, martingales, optional sampling/optional stopping and Brownian motion. This is entirely too ambitious a reading list to squeeze into the 40 or so pages allocated for all of this, in the opinion of this reviewer. The author places some prerequisite material in the appendix chapter.
Chapter 5 is a much more down-to-earth treatment of genuine applications of Markov chains. Birth/Death processes in biology, queuing networks in information theory, inventory management in operations research, and Markov decision processes are introduced via a series of very nice toy examples. This chapter wraps up with a nice discussion of simulation and the method of Markov chain Monte Carlo.
If the next edition of this book removes chapter 4 and replaces it with treatment of an actual real-world problem (or two) using genuine data sets, this reviewer would be happy to rate that edition 5 stars.
I found chapters 1-3 to be fairly useful in achieving the goal of further educating myself on Markov chains, but the book after that fell quite bit short of my expectations. Perhaps my level of mathematical maturity isn't enough, or I'm the wrong audience (i.e. someone that doesn't especially care if the state-space is a countable set or if the Q Matrix is explosive), but I did find some sections of the book to be difficult to comprehend, and just ended up skipping a lot of the proofs due to lack of readability.
This book could appeal to a much wider audience if the first 3 chapters spent more time discussing the theorems, and then combined chapters 4 and 5 into some fully worked out numerical examples from each of the different major areas of application.
The Monte Carlo section with Hastings and Metropolis algorithms were especially disappointing, and they weren't very instructive as to how to actually implement these algorithms on a computer using a real data set, which was my main interest.
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