In this talk we introduce a notion of stochastic viscosity solution
for a class of fully nonlinear 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.