Discrete Markov Chain Pdf Download
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Sheldon Ross, Introduction to Probability Models, 2006 (Chapter 4) and Stochastic Processes,1995 (Chapter 4) (Each of these books contains a readable chapter on Markov chains and many nice examples. The author does a good job of making difficult concepts seem fairly simple.) See also, Sheldon Ross and Erol Pekoz, A Second Course in Probability, 2007 (Chapter 5 gives a readable treatment of Markov chains and covers many of the topics in our course. In other chapters this book provides a gentle introduction to probability and measure theory.) Charles Grinstead and Laurie Snell Introduction to Probability Second edition, 1997 (freely available to download). This book is also quite easy to read. The authors have good insight and you will find some gems here. Chapter 11 is on Markov Chains. This book it is particulary interesting about absorbing chains and mean passage times. There are many nice exercises, some notes on the history of probability, and on pages 464-466 there is information about A. A. Markov and the early development of the field. There are two distinct approaches to the study of Markov chains. One emphasises probabilistic methods (as does Norris's book and our course); another is more matrix-based, as it this book. The probabilistic methods are more satisfying, but it is good to know something about the matrix methods too.) Takis Konstantopoulos has a nice set of course notes on Markov Chains and Random Walks, 2009, at a somewhat more in-depth level than our course. You might like to browse through his notes. David Aldous and Jim Fill Reversible Markov Chains and Random Walks on Graphs, 1994-2001 (This monograph is freely available and a great souce of delightful information and insightful comment. It covers much more advanced topics that in our course. However, Chapters 1-3 are well within your grasp, and to read them will deepen your understanding.) Peter Doyle and Laurie Snell Random walks and electric networks, 2006 (freely available to download. You could read this (easy to understand) paper to learn more about the interesting connection between recurrence/transience properties of random walks and resistence in electrical network, as I will briefly discuss in Lecture 12. David Levin, Yuval Peres and Elizabeth Wilmer Markov Chains and Mixing Times, 2008. Chapters 1 and 2 nicely summarise most of the content of our course in a small number of pages. However, I reference this textbook mainly because it is a good place to read about some of the fascinating topics within the field of Markov chains that interest researchers today. For example, Chapter 5 on Coupling, will tell you how the ideas we used in Lecture 9 can be extended. This is a book you wiill want to read if ever go beyond undergraduate study in this field. The PageRank citation ranking: bringing order to the web (by Lawrence Page, Sergey Brin, Rajeev Motwani, and Terry Winograd, 1998) describes the workings of the Google PageRank algorithm and the part that Markov chains play in this. This is discussed in brief in Lecture 8, Example 8.6 (random surfer). See also the Wikipedia article about PageRank. Peter Winkler, Mathematical Mind Benders, 2007. This is not a book on Markov Chains, but a collection of mathematical puzzles that I recommend. Many of the puzzles are based in probability. It includes the \"Evening out the Gumdrops\" puzzle that I discuss in lectures, and lots of other great problems. He has an earlier book also, Mathematical Puzzles: a Connoisseur's Collection, 2003. Frederick Mosteller, 50 Challenging Problems in Probability, with Solutions, 1987. This is a classic book which anyone who is interested in probability should enjoy. David Aldous has an interesting page of his reviews of many non-technical books related to probability. You might enjoy thinking about the points made in his posting:Presenting probability via math puzzles is harmful. 153554b96e
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