Quasilinear Stochastic PDEs with two obstacles: Probabilistic approach

TL;DR

This paper establishes existence and uniqueness for a class of quasilinear stochastic PDEs with two obstacles using a probabilistic approach based on backward doubly stochastic differential equations.

Contribution

It introduces a novel probabilistic method to solve two-obstacle quasilinear stochastic PDEs, extending existing techniques to this complex setting.

Findings

Proved existence and uniqueness of solutions.

Developed a probabilistic framework for two-obstacle problems.

Extended BDSDE methods to handle multiple obstacles.

Abstract

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).