Reflected backward stochastic partial differential equations in a convex domain

Abstract

This paper is concerned with the reflected backward stochastic partial differential equations, taking values in a convex domain in Rk. The existence and uniqueness of solution are studied under both the super-parabolic and parabolic conditions. In the degenerate parabolic case the connection between reflected backward stochastic partial differential equations and reflected forward backward stochastic differential equations is established.