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An Introduction to Markov Processes: 230 (Graduate Texts in Mathematics, 230) - Softcover

 
9783540234517: An Introduction to Markov Processes: 230 (Graduate Texts in Mathematics, 230)

Synopsis

This book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable state space. It should be accessible to students with a solid undergraduate background in mathematics, including students from engineering, economics, physics, and biology. Topics covered are: Doeblin's theory, general ergodic properties, and continuous time processes. A whole chapter is devoted to reversible processes and the use of their associated Dirichlet forms to estimate the rate of convergence to equilibrium.

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Review

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)

About the Author

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.

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  • PublisherSpringer
  • Publication date2005
  • ISBN 10 3540234519
  • ISBN 13 9783540234517
  • BindingPaperback
  • LanguageEnglish
  • Number of pages190

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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Provides a more accessible introduction than other books on Markov processes by emphasizing the structure of the subject and avoiding sophisticated measure theoryLeads the reader to a rigorous understanding of basic theory 196 pp. Englisch. Seller Inventory # 9783540234517

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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Seller Inventory # 9783540234517

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