To Brownian Motion — Lectures From Markov Processes

: Covers the basic Markov property, transition functions, optional (stopping) times, and fundamental martingale theorems.

: 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. Lectures from Markov Processes to Brownian Motion

: Explores the connection between martingales and Markov processes, Feller processes, and the strong Markov property. : Covers the basic Markov property, transition functions,

: 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 : Covers the basic Markov property