Speaker:  Rohini Kumar, Wayne State University

Nov 14, 1-2 pm

FAB 1285 (in person)

Title: Connections between Probability and PDEs

Abstract:

We will look at some examples of PDEs that can be solved by running a Brownian motion. I will begin with a very brief introduction to Brownian motion (BM) and Ito’s formula. These form the building blocks for stochastic representations of solutions to linear PDEs. (There are stochastic representations of quasilinear PDEs via Backward Stochastic Differential Equations, but this is beyond the scope of this talk.) Time permitting we will look at some applications like stochastic control and optimal stopping problems in finance, and the connection between the study of large deviations in Probability and Hamilton-Jacobi-Bellman equations. I will not assume any knowledge of Probability beyond elementary undergraduate probability.