The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration ...

Topics: As it says in the title, this is a topics course. Specific material will depend on time and interest levels, but some of the general topics I have in mind are: Markov Chains, Random Matrix ...

It covers recent applications, including density formulas, regularity of probability laws, central and non-central limit theorems for Gaussian functionals, convergence of densities and non-central ...