MATH 6050 - Mathematical Probability II

This course is a rigorous introduction to the fundamentals of stochastic processes. Stochastic processes model the evolution of a random quantity over time and are used in a wide variety of applications. The goal is to provide students with a solid foundation in the fundamental mathematics of the subject. Students will learn theory, techniques, and applications related to Markov chains, stationary processes, Brownian motion, weak convergence, and other related topics (e.g. stochastic calculus, connections to linear PDEs, one-dimensional and multidimensional diffusion, stochastic differential equations, branching Brownian motion, random walk in random environment; etc)