Probabilistic Representation for Viscosity Solution of Fully nonlinear Stochastic PDEs

Anis Matoussi (Universite du Maine, Le Mans)
Thursday, May 12, 2016 - 5:00pm
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

We propose a wellposedness theory for a class of second order backward doubly stochastic differential equation (2BDSDE). We prove existence and uniqueness of the solution under a Lipschitz type assumption on the generator, and we investigate the links between the 2BDSDEs and a class of parabolic fully nonlinear Stochastic PDEs. Precisely, we show that the Markovian solution of 2BDSDEs provide a probabilistic interpretation of the classical and stochastic viscosity solution of fully nonlinear SPDEs. This presentation includes some applications in pathwise stochastic control problems.