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Article Dans Une Revue Probability Theory and Related Fields Année : 2019

Probabilistic interpretation for solutions of fully nonlinear stochastic PDEs

Résumé

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.

Dates et versions

hal-01481372 , version 1 (02-03-2017)

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Anis Matoussi, Dylan Possamaï, Wissal Sabbagh. Probabilistic interpretation for solutions of fully nonlinear stochastic PDEs. Probability Theory and Related Fields, 2019, 174, pp.177-233. ⟨10.1007/s00440-018-0859-4⟩. ⟨hal-01481372⟩
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