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Probabilistic Interpretation for Solutions of Fully Nonlinear SPDEs

Speaker

Anis Matoussi, University du Maine, Le Mans, France

Time

2018.03.13 16:00-17:00

Venue

Middle Lecture Room, Math Building

Abstract

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).