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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 measuretheoretic 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. | Cambridge studies in advanced mathematics 100 Markov Processes Gaussian Processes and Local Times MICHAEL B. MARCUS Cambridge This page intentionally left blank CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS 100 MARKOV PROCESSES GAUSSIAN PROCESSES AND LOCAL TIMES 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 .
