Probabilistic interpretation for solutions of fully nonlinear stochastic PDEs
成果类型：
Article
署名作者：
Matoussi, Anis; Possamai, Dylan; Sabbagh, Wissal
署名单位：
Le Mans Universite; Columbia University; Universite Paris Saclay
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-018-0859-4
发表日期：
2019
页码：
177-233
关键词：
摘要：
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 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.
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