Sebastien Roch (Spring 2018):
This is the second semester of an introductory course on graduate level mathematical probability theory. Math/Stat 734 covers core topics in discrete-time and continuous-time stochastic processes. This includes Markov chains, point processes, Markov processes, stationary processes and ergodic theory, Brownian motion, and if time permits diffusion processes. Most of the material is contained in Chapters 6 through Chapter 8 of Probability: Theory and Examples by Durrett.