This is the second half of a year-long introduction to probability theory at the graduate level. We will pick up where MATH 6710 left off and a general knowledge of that material will be assumed. The material to be covered includes martingales, Markov chains, and Brownian motion. Depending on student interest, we will also discuss topics from ergodic theory and/or stochastic calculus.
Probability: Theory and Examples, 4th Edition by Rick Durrett