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An Introduction to Markov Processes

By: Stroock, Daniel W [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Graduate Texts in Mathematics: 230Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005.Description: XIV, 178 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540269908.Subject(s): Mathematics | Probabilities | Mathematics | Probability Theory and Stochastic ProcessesDDC classification: 519.2 Online resources: Click here to access online
Contents:
Random Walks A Good Place to Begin -- Doeblin's Theory for Markov Chains -- More about the Ergodic Theory of Markov Chains -- Markov Processes in Continuous Time -- Reversible Markov Processes -- Some Mild Measure Theory.
In: Springer eBooksSummary: 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.
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Item type Current location Call number Status Date due Barcode Item holds
E books E books PK Kelkar Library, IIT Kanpur
Available EBK6416
Total holds: 0

Random Walks A Good Place to Begin -- Doeblin's Theory for Markov Chains -- More about the Ergodic Theory of Markov Chains -- Markov Processes in Continuous Time -- Reversible Markov Processes -- Some Mild Measure Theory.

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.

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