二重バリア付後退二重確率微分方程式と制約付確率偏微分方程式との関連付け

抄録

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.