Reflected generalized backward doubly SDEs with jumps under stochastic conditions: Beyond right-continuity

RGBSDEs with jumps under stochastic conditions: Beyond right-continuity

Abstract

In this paper, we study reflected generalized backward doubly stochastic differential equations where the obstacle is not necessarily right-continuous, and the noise is driven by two mutually independent Brownian motions and an independent integer-valued random measure. Under stochastic monotonicity, Lipschitz, and linear growth conditions, we establish the existence and uniqueness of a solution. Additionally, we prove a comparison principle for such equations.