Existence of solution for Mean-field Reflected Discontinuous Backward Doubly Stochastic Differential Equation

Abstract

In this paper we prove the existence of a solution for mean-field reflected backward doubly stochastic differential equations (MF-RBDSDEs) with one continuous barrier and discontinuous generator (left-continuous). By a comparison theorem establish here for MF-RBDSDEs, we provide a minimal or a maximal solution to MF-RBDSDEs.

Keywords

• reflected backward doubly stochastic differential equations
• mean-field
• minimal solution
• comparison theorem
• discontinuous generator
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