Markov Processes, Gaussian Processes, and Local Times

by Marcus, Michael B.; Rosen, Jay

• ISBN13: 9781107403758
• ISBN10: 1107403758
• Edition: Revised
• Format: Paperback
• Copyright: 2011-10-27
• Publisher: Cambridge Univ Pr

Summary

Written by two 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 for 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 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.

Table of Contents

Introduction

Brownian motion and Ray-Knight theorems

Markov processes and local times

Constructing Markov processes

Basic properties of Gaussian processes

Continuity and boundedness

Moduli of continuity

Isomorphism theorems

Sample path properties of local times

p-Variation

Most visited site

Local times of diffusions

Associated Gaussian processes

Appendices

Kolmogorov's theorem for path continuity

Bessel processes

Analytic sets and the projection theorem

Hille-Yosida theorem

Stone-Weierstrass theorems

Independent random variables

Regularly varying functions

Some useful inequalities

Some linear algebra

References

Index

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