Irregular barrier reflected BDSDEs with general jumps under stochastic Lipschitz and linear growth conditions

Abstract

In this paper, a solution is given to reflected backward doubly stochastic differential equations when the barrier is not necessarily right-continuous, and the noise is driven by two independent Brownian motions and an independent Poisson random measure. The existence and uniqueness of the solution is shown, firstly when the coefficients are stochastic Lipschitz, and secondly by weakening the conditions on the stochastic growth coefficient.

Keywords

• Reflected backward doubly stochastic differential equations
• irregular barrier
• Mertens decomposition
• stochastic Lipschitz condition
• stochastic linear growth condition