The obstacle problem for quasilinear stochastic PDE's

TL;DR

This paper establishes existence and uniqueness results for the obstacle problem in quasilinear parabolic stochastic PDEs, utilizing backward doubly stochastic differential equations for a probabilistic solution approach.

Contribution

It introduces a novel method combining probabilistic interpretation with backward doubly stochastic differential equations for solving the obstacle problem.

Findings

Proves existence and uniqueness of solutions.

Develops a probabilistic framework for the obstacle problem.

Connects stochastic PDEs with backward doubly stochastic differential equations.

Abstract

We prove an existence and uniqueness result for the obstacle problem of quasilinear parabolic stochastic PDEs. The method is based on the probabilistic interpretation of the solution by using the backward doubly stochastic differential equation.