Quasilinear Stochastic PDEs with two obstacles: Probabilistic approach

Laurent Denis (1) , Anis Matoussi (1) , Jing Zhang (2)

1 LMM - Laboratoire Manceau de Mathématiques
2 School of Mathematical Sciences [Fudan]

We prove an existence and uniqueness result for two-obstacle problem for quasilinear Stochastic PDEs (DOSPDEs for short). The method is based on the probabilistic interpretation of the solution by using the backward doubly stochastic differential equations (BDSDEs for short).

Mots clés: stochastic partial differential equations; two-obstacle problem; backward doubly stochastic differential equations; regular potential; regular measure AMS 2000 subject classifications: Primary 60H15; 35R60; 31B150

Domaines: Probabilités [math.PR]

Laurent Denis, Anis Matoussi, Jing Zhang. Quasilinear Stochastic PDEs with two obstacles: Probabilistic approach. Stochastic Processes and their Applications, 2021, ⟨10.1016/j.spa.2020.11.002⟩. ⟨hal-03040517⟩