: A unique feature of the expanded edition is the inclusion of informal sections called "Fireside Chats," which provide historical context and intuitive summaries of complex topics. Target Audience
: The 2005 version adds 10 new chapters by John Walsh, focusing on Ray processes , time reversal , and duality . Lectures from Markov Processes to Brownian Motion
: Covers the basic Markov property, transition functions, optional (stopping) times, and fundamental martingale theorems. : A unique feature of the expanded edition
: Focuses on spatial homogeneity and the specific sample path properties of Brownian motion. : Focuses on spatial homogeneity and the specific
: While it aims to be self-contained, it frequently refers to Chung’s other classic, A Course in Probability Theory , for discrete-parameter martingale foundations.
: Discusses the analytical side of the theory, including the relationship between probability and potential theory. Key Features & Style 💡