An Introduction to Modeling Random Walks

Abstract: Modern probability theory is founded upon measure theory. We will show how to take advantage of this framework to rigorously model stochastic processes such as coin flipping and random walks. For such models, what questions can we answer, and what applications are there? Aside from one recent research application, this will primarily be an expository talk, not a research talk. Similar content can be found in the book Probability with Martingales by David Williams.