Markov Processes, Gaussian Processes, and Local Times

Erscheinungsjahr 2016
ISBN: 978-0-521-86300-1
Verlag: Cambridge University Press

Buch, Englisch, Band 100, 630 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 1163 g

Reihe: Cambridge Studies in Advanced Mathematics

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.

Autoren/Hrsg.

Marcus, Michael B.

Rosen, Jay

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse

Inhaltsverzeichnis

1. Introduction
2. Brownian motion and Ray-Knight theorems
3. Markov processes and local times
4. Constructing Markov processes
5. Basic properties of Gaussian processes
6. Continuity and boundedness
7. Moduli of continuity
8. Isomorphism theorems
9. Sample path properties of local times
10. p-Variation
11. Most visited site
12. Local times of diffusions
13. Associated Gaussian processes
Appendices: A. Kolmogorov's theorem for path continuity
B. Bessel processes
C. Analytic sets and the projection theorem
D. Hille-Yosida theorem
E. Stone-Weierstrass theorems
F. Independent random variables
G. Regularly varying functions
H. Some useful inequalities
I. Some linear algebra
References
Index.

Über Autor(innen)

Marcus, Michael B.
Michael B. Marcus is Professor of Mathematics at City College and The CUNY Graduate Center. A leading expert on stochastic processes, he has published over one hundred research papers and delivered over 200 invited lectures. He is a Fellow of the Institute of Mathematical Statistics.

Rosen, Jay
Jay Rosen is Professor of Mathematics at The Graduate Center and the College of Staten Island, City University of New York. A leading expert on stochastic processes, he has published over eighty research papers. He is a Fellow of the Institute of Mathematical Statistics.