In this lecture, we put together many of the topics covered throughout the term: martingales; Markov chains; countable state Markov processes; reversibility for Markov processes; random walks; and Wald's identity for two thresholds.

Sequential hypothesis testing is viewed as a random walk example. Threshold hypothesis tests are distinguished from random walk thresholds. Random walk threshold probabilities are analyzed by Chernoff bounds.

This lecture continues our conversation on Martingales and covers stopped martingales, Kolmogorov submartingale inequality, martingale convergence theorem, and more.