Department of Mathematics

Speaker: Jin Ma
Title: Viscosity Solutions for Forward Stochastic Partial Differential Equations and Path-Dependent Partial Differential Equations
Affiliation: University of Southern California
Date: Friday, March 21, 2014
Place and Time: Room 101, Love Building, 3:35-4:30 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. In this talk we introduce a notion of stochastic viscosity solution for a class of fully nonlinear Stochastic PDE (SPDEs) and the corresponding Path-dependent PDEs (PPDEs). The definition is based on our new accompanying work on the pathwise stochastic Taylor expansion, using a variation of the path- derivatives initiated by Dupire. As a consequence this new definition of the viscosity solution is directly in the pathwise sense, without having to invoke the stochastic characteristics for the localization. The issues of consistency, stability, comparison principles, and ultimately the well-posedness of the stochastic viscosity solutions will be discussed under this new framework.

This is a joint work with Rainer Buckdahn and Jianfeng Zhang.