Markov Processes Gaussian Processes And Local Times
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Markov Processes, Gaussian Processes, and Local Times
Author: Michael B. Marcus
language: en
Publisher: Cambridge University Press
Release Date: 2006-07-24
A readable 2006 synthesis of three main areas in the modern theory of stochastic processes.
Markov Processes, Gaussian Processes, and Local Times
Author: Michael B. Marcus
language: en
Publisher: Cambridge University Press
Release Date: 2006-07-24
This book was first published in 2006. Written by two of the foremost researchers in the field, this book studies the local times of Markov processes by employing isomorphism theorems that relate them to certain associated Gaussian processes. It builds to this material through self-contained but harmonized 'mini-courses' on the relevant ingredients, which assume only knowledge of measure-theoretic probability. The streamlined selection of topics creates an easy entrance for students and experts in related fields. The book starts by developing the fundamentals of Markov process theory and then of Gaussian process theory, including sample path properties. It then proceeds to more advanced results, bringing the reader to the heart of contemporary research. It presents the remarkable isomorphism theorems of Dynkin and Eisenbaum and then shows how they can be applied to obtain new properties of Markov processes by using well-established techniques in Gaussian process theory. This original, readable book will appeal to both researchers and advanced graduate students.
Séminaire de Probabilités XLII
Author: Catherine Donati-Martin
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-06-29
The tradition of specialized courses in the Séminaires de Probabilités is continued with A. Lejay's Another introduction to rough paths. Other topics from this 42nd volume range from the interface between analysis and probability to special processes, Lévy processes and Lévy systems, branching, penalization, representation of Gaussian processes, filtrations and quantum probability.