Connection with Double Barrier Backward Doubly Stochastic Differential Equations and Obstacle Stochastic Partial Differential Equations

Abstract

In this paper, we establish the existence and uniqueness of a solution to a double barrier backward doubly stochastic differential equation (DB-BDSDE). This would be proved by using the “penalization method” as in the case of a single barrier backward doubly stochastic differential equation. Additionally, we give a connection between DB-BDSDE and obstacle stochastic partial differential equation (SPDE). To achieve this, we claim that through the existence of a stochastic viscosity solution to obstacle SPDE associated with DB-BDSDE using the so-called Doss–Sussmann transformation.