The Obstacle Problem for Quasilinear Stochastic Integral-Partial Differential Equations

TL;DR

This paper establishes existence and uniqueness for the obstacle problem in quasilinear stochastic integral-partial differential equations, using backward doubly SDEs with jumps for a probabilistic approach.

Contribution

It introduces a novel probabilistic method employing backward doubly SDEs with jumps to solve the obstacle problem for these complex equations.

Findings

Proved existence and uniqueness of solutions.

Developed a probabilistic framework for the problem.

Applied backward doubly SDEs with jumps to the obstacle problem.

Abstract

We prove an existence and uniqueness result for the obstacle problem for quasilinear stochastic integral-partial differential equations. Our method is based on the probabilistic interpretation of the solution using backward doubly SDEs with jumps.