The obstacle problem for quasilinear stochastic PDEs with Neumann boundary condition

Abstract

We prove the existence and uniqueness of solution to obstacle problem for quasilinear stochastic partial differential equations with Neumann boundary condition. Our method is based on the analytical techniques coming from parabolic potential theory. The solution is expressed as a pair [Formula: see text] where [Formula: see text] is a predictable continuous process which takes values in a proper Sobolev space and [Formula: see text] is a random regular measure satisfying minimal Skohorod condition.