Probabilistic interpretation for solutions of fully Nonlinear Stochastic PDEs
Probability
2016-10-14 v2
Abstract
In this article, 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 our 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.
Keywords
Cite
@article{arxiv.1412.5548,
title = {Probabilistic interpretation for solutions of fully Nonlinear Stochastic PDEs},
author = {Anis Matoussi and Dylan Possamai and Wissal Sabbagh},
journal= {arXiv preprint arXiv:1412.5548},
year = {2016}
}
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