Reflected backward stochastic partial differential equations with jumps in a convex domain

Abstract

This paper is concerned with a class of multi-dimensional reflected backward stochastic partial differential equations (BSPDE for short), taking values in a convex domain in Rk, which are driven by an infinite dimensional Brownian motion and an independent compensated Poisson random measure. Existence and uniqueness of the solution to this class of reflected BSPDEs are proved. Penalization method plays an important role.