English

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}
}

Comments

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R2 v1 2026-06-22T07:35:36.252Z