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.

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.'

Source: 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.'

Source: Journal of the American Statistical Association