Markov Processes, Gaussian Processes, and Local Times

This 2006 work by leading researchers explores advancements in stochastic process theory, connecting Markov and Gaussian processes. It offers accessible mini-courses, making it suitable for researchers and advanced graduate students.

Markov Processes, Gaussian Processes, and Local Times is a comprehensive exploration of stochastic process theory, authored by two leading researchers in the field. The book effectively bridges the gap between well-established Gaussian processes and the less understood Markov processes. It is designed for both researchers and advanced graduate students, making it accessible with only a foundational knowledge of measure-theoretic probability.

The text is structured around self-contained mini-courses that introduce essential concepts and gradually lead the reader into more complex topics. It begins with the fundamentals of Markov process theory, followed by an examination of Gaussian process theory, which includes a focus on sample path properties. This thoughtful progression allows readers to build a solid understanding before delving into advanced results, ultimately guiding them to the forefront of contemporary research.

A significant contribution of the book is its presentation of the isomorphism theorems developed by Dynkin and Eisenbaum. These theorems are pivotal in linking Markov processes to associated Gaussian processes, allowing for the discovery of new properties of Markov processes through established techniques in Gaussian theory. Overall, this 2006 publication serves as a valuable resource, synthesizing key areas of modern stochastic process theory in a manner that is both engaging and informative.