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Graduate Seminar

Yangxi Ou
Carnegie Mellon University
Title: Introducing BSDE by BS of DE

Abstract: It is well-known that there is a "dictionary" between PDE and stochastic calculus. For example, harmonic functions in PDE correspond to martingale processes in probability. One of the most celebrated results is the Feynman-Kac formula, expressing the solutions to elliptic/parabolic equations in terms of expectations of functionals of diffusion processes (which unfortunately is the farthest point most graduate students stop connecting both fields). In this talk, we reinterpret the Feynman-Kac formula as the elliptic/parabolic version of the method of characteristics in solving first order PDEs. Inspired by this perspective, we introduce Backward Stochastic Differential Equations (BSDE), in the hope to solve nonlinear elliptic/parabolic equations. Like almost every talk of DEs, the meaning of solutions and the trial space will be defined, and the unique existence of solutions will be given (under assumptions). Further properties and/or generalizations will be discussed, if time permits.

Date: Tuesday, April 4, 2017
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Yangxi Ou
Note: Video on Youtube: https://youtu.be/9BcHeKtBWKQ