Graduate Texts in Mathematics

An Introduction to Markov Processes

Authors: Stroock, Daniel W.

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About this Textbook

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

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

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 (1 chapters)

Buy this book

eBook $29.99
price for USA (gross)
  • ISBN 978-3-540-26990-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.95
price for USA
  • ISBN 978-3-540-23451-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Markov Processes
Authors
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