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Probabilistic interpretation for solutions of fully nonlinear stochastic PDEs

Matoussi, Anis; Possamaï, Dylan; Sabbagh, Wissal (2018), Probabilistic interpretation for solutions of fully nonlinear stochastic PDEs, Probability Theory and Related Fields. 10.1007/s00440-018-0859-4

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01481372
Date
2018
Journal name
Probability Theory and Related Fields
Publisher
Springer
Publication identifier
Metadata
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Author(s)
Matoussi, Anis

Possamaï, Dylan

Sabbagh, Wissal
Abstract (EN)
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.
Subjects / Keywords
PDEs; 2BDSDEs