Probabilistic interpretation for solutions of fully Nonlinear Stochastic\n PDEs

2014/12/17 by Anis Matoussi, Matoussi, Anis, Dylan Possamaï +3 · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #35H60 #60G46 #60H15 #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1412.5548

openalex publication_date 2014/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we propose a wellposedness theory for a class of second\norder backward doubly stochastic differential equation (2BDSDE). We prove\nexistence and uniqueness of the solution under a Lipschitz type assumption on\nthe generator, and we investigate the links between our 2BDSDEs and a class of\nparabolic fully nonLinear Stochastic PDes. Precisely, we show that the\nMarkovian solution of 2BDSDEs provide a probabilistic interpretation of the\nclassical and stochastic viscosity solution of fully nonlinear SPDEs.\n

Citations

• Capacities, Measurable Selection and Dynamic Programming Part II: Application in Stochastic Control Problems
• Obstacle problem for SPDE with nonlinear Neumann boundary condition via reflected generalized backward doubly SDEs

Cited by

• Stochastic PDEs driven by G-Brownian motion and the associated Backward Doubly Stochastic Differential Equations

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