Stroock An Introduction to Markov Processes

2005
ISBN: 978-3-540-26990-8
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 230, 185 Seiten, eBook

Reihe: Graduate Texts in Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Stroock, Daniel W.

Inhaltsverzeichnis

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.

Über Autor(innen)

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.