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Markov Chains (Cambridge Series in Statistical and Probabilistic Mathematics)

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J. R. Norris (Author)
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J. R. Norris (Author)
3.3 out of 5 stars 11 customer reviews
ISBN-13: 978-0521633963
ISBN-10: 0521633966
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Product Details

  • 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 (11 customer reviews)
  • Amazon Best Sellers Rank: #979,832 in Books (See Top 100 in Books)

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Customer Reviews

Top Customer Reviews

3.0 out of 5 starsGood introductory treatment, but has some issues
By Paul Thurston on May 6, 2005
Format: Paperback Verified Purchase
This book has two principal aims. In the first half of the book, the aim is the study of discrete time and continuous time Markov chains. The first part of the text is very well written and easily accessible to the advanced undergraduate engineering or mathematics student.

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.Read more ›
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3.0 out of 5 starsUnique but poorly written
By Diff D on June 6, 2009
Format: Paperback
This is a unique book that bridges the gap between undergraduate and graduate treatment but only in the first three chapters. It does require a number of preparatory courses, from multivariate calculus, linear algebra, differential equations to solid understanding of at least undergraduate level of probability, preferable something like Williams' "Probability with Martingales" which Norris seems to refer to. In the United States this is a preparation that is available only in elite schools as many do not even require differential equations for mathematics major while probability is indeed a rare feat to see in mostly pathetic US undergraduate math curricula.

Unfortunately the book is not well written and that is the main reason why it is not more popular than it is. The text beyond first three chapters is largely useless and hard to sort out, with very little care about readability.

There are moments in the text when the author assumes his reader is quite telepatic as some proofs are rather sketchy, and some are even erroneous. Given the first edition that is forgivable although fairly annoying on occasion. The book also contains quite a few misprints adding to confusion. In its scope, the Chapter 1 on discrete Markov Chains is charming, rigorous, and accessible. I have not seen elementary Markov Chains treatment with such a solid level of rigor. Intuition is paired with precise proofs. Chapter 2 on the other hand is somewhat strange and too lax but with important treatment of special cases of Markov Processes to motivate the theory with the main result of definition of continuous Markov Chain. Prior to that the author has chosen "holding times - jump process" presentation which is intuitivelly easier to understand although the definition itself is more intricate.Read more ›
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4.0 out of 5 starsVery useful if you have a good mathematical background!
By A Customer on May 23, 2001
Format: Hardcover
I found this book very useful for a better comprehension of Markov chains and for understanding the theory, but you need a very good knowledge of mathematics like calculus, matrix, differential equations and statistics in order to keep going in your reading. Don't expect full numerical examples, be ready for demostrations! I recommend it for students interested in stochastic processes or looking a good approach to the basis of Markov processes.
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2.0 out of 5 starsAnnoying Book
By Stephen P Gibert on August 17, 2013
Format: Paperback
The author seems to think that being obscure will somehow benefit the reader. If that were the case, the benefit would be tremendous, as this book makes simple things difficult in many places. The choice of topics is good, and there is an elegance to the mathematics which shows that certainly some effort was put forward in that direction. But there are a number of theorems which are so poorly stated that the proofs have to be examined carefully just to tell what is being proved, making for a frustrating and unnecessarily time consuming experience. If a second edition were done with a little more care this might be a good book, but I think that this book, as it stands, isn't worth the trouble.
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3.0 out of 5 starsgood, sophisticated book
By mathstudent1 on December 3, 2011
Format: Paperback Verified Purchase
Good summary of Markov chains for someone with a thorough background in stochastic processes; however, it lacks the readability for a beginner in the subject, even one with a couple probability courses under his/her belt.
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4.0 out of 5 starsEverything about Markov Chains
By Hannah Ford on November 23, 2004
Format: Paperback
I used this book in my second year of Undergraduate Study and I would recommend it to anyone wanting a clear, consise book on Markov Chains. It covers a broad range of topics, and has many questions to check your understanding.

However, There are NOT answers to these questions so don't use this if you're looking for an easy way out of a homework sheet!

The best book I've read on the subject, without a doubt
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