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- About this Textbook
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To some extent, it would be accurate to summarize the contents of this book as an intolerably protracted description of what happens when either one raises a transition probability matrix P (i. e. , all entries (P)»j are n- negative and each row of P sums to 1) to higher and higher powers or one exponentiates R(P — I), where R is a diagonal matrix with non-negative entries. Indeed, when it comes right down to it, that is all that is done in this book. However, I, and others of my ilk, would take offense at such a dismissive characterization of the theory of Markov chains and processes with values in a countable state space, and a primary goal of mine in writing this book was to convince its readers that our offense would be warranted. The reason why I, and others of my persuasion, refuse to consider the theory here as no more than a subset of matrix theory is that to do so is to ignore the pervasive role that probability plays throughout. Namely, probability theory provides a model which both motivates and provides a context for what we are doing with these matrices. To wit, even the term "transition probability matrix" lends meaning to an otherwise rather peculiar set of hypotheses to make about a matrix.
- About the authors
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The author has held positions at NYU, the Univresity of Colorado, and MIT. In addition, he has visited and lectured at many universities throughout the world. He has authored several book bout various aspects of probability theory.
- Reviews
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From the reviews:
“The book under review … provides an excellent introduction to the theory of Markov processes … . An abstract mathematical setting is given in which Markov processes are then defined and thoroughly studied. Because of this the book will basically be of interest to mathematicians and those who have at least a good knowledge of undergraduate analysis and probability theory. … The proofs are clearly written and explanations are not too concise which makes this book indeed very useful for a graduate course.” (Stefaan De Winter, Bulletin of the Belgian Mathematical Society, Vol. 15 (1), 2008)
- Table of contents (6 chapters)
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Random Walks A Good Place to Begin
Pages 1-22
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Doeblin's Theory for Markov Chains
Pages 23-44
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More about the Ergodic Theory of Markov Chains
Pages 45-74
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Markov Processes in Continuous Time
Pages 75-106
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Reversible Markov Processes
Pages 107-144
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Table of contents (6 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- An Introduction to Markov Processes
- Authors
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- Daniel W. Stroock
- Series Title
- Graduate Texts in Mathematics
- Series Volume
- 230
- Copyright
- 2005
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-540-26990-8
- DOI
- 10.1007/b138428
- Softcover ISBN
- 978-3-540-23451-7
- Series ISSN
- 0072-5285
- Edition Number
- 1
- Number of Pages
- XIV, 178
- Topics
