Description
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.
A readable 2006 synthesis of three main areas in the modern theory of stochastic processes.
About the Author
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. 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.
Reviews
Review of the hardback: 'This is a masterly written text which should be accessible to advanced graduate students and non-specialists. For the researcher interested in Gaussian processes or local times it will become an indispensable standard resource.' Zentralblatt MATH
Review of the hardback: 'The authors make every effort to make the material accessible, and the proofs presented are often much easier than the original ones. The material is well organized and well presented.' Journal of the American Statistical Association
Book Information
ISBN 9780521863001
Author Michael B. Marcus
Format Hardback
Page Count 632
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 960g
Dimensions(mm) 229mm * 152mm * 40mm
A readable 2006 synthesis of three main areas in the modern theory of stochastic processes.
About the Author
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. 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.
Reviews
Review of the hardback: 'This is a masterly written text which should be accessible to advanced graduate students and non-specialists. For the researcher interested in Gaussian processes or local times it will become an indispensable standard resource.' Zentralblatt MATH
Review of the hardback: 'The authors make every effort to make the material accessible, and the proofs presented are often much easier than the original ones. The material is well organized and well presented.' Journal of the American Statistical Association
Book Information
ISBN 9780521863001
Author Michael B. Marcus
Format Hardback
Page Count 632
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 960g
Dimensions(mm) 229mm * 152mm * 40mm
