: Focuses on spatial homogeneity and the specific sample path properties of Brownian motion.
: Explores the connection between martingales and Markov processes, Feller processes, and the strong Markov property.
: 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
: Researchers in mathematical physics and analysis use it as a reference for Hunt processes and Brownian motion sample paths.
: 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 : Focuses on spatial homogeneity and the specific
: A deeper dive into specialized processes, hitting times, and potential theory (excessive functions and balayage).
: Chung is known for an "explanatory rather than dogmatic" style, prioritizing clarity over dense formalism. : Researchers in mathematical physics and analysis use
: 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.