MA 529: Stochastic Processes

This course is designed to introduce students to continuous-time stochastic processes. Stochastic processes play a central role in a wide range of applications from signal processing to generative A.I. to finance and offer an alternative novel viewpoint to several areas of mathematical analysis, such as partial differential equations and potential theory. The first part of this course will cover the theory of stochastic processes, including martingales, Brownian motion and diffusions, stochastic differential equations, stochastic (Ito) calculus, and Markov Chains. The second part of the course will cover applications chosen by the instructor, such as simulation of stochastic processes, randomized algorithms and applications, stochastic optimization, spatial-temporal statistics, nonlinear filtering, applications to deep learning and generative A.I., or applications in finance. Students are encouraged to ask the instructor for a list of the covered applications.