Reflected Discontinuous Backward Doubly Stochastic Differential Equation With Poisson Jumps (1704.06927v1)

Abstract: In this paper{}we prove the existence of a solution for reflected backward doubly stochastic differential equations with poisson jumps (RBDSDEPs) with one continuous barrier where the generator is continuous and also we study the RBDSDEPs with a linear growth condition and left continuity in $y$ on the generator. By a comparison theorem established here for this type of equation we provide a minimal or a maximal solution to RBDSDEPs.