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.
General
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