Speaker: Jin Ma
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.