Anis Matoussi, University du Maine, Le Mans, France
Middle Lecture Room, Math Building
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. The talk is based on a joint work with Dylan Possamai (Columbia University) and Wissal Sabbagh (University of Evry-Paris-Saclay).