倒向重随机微分方程解的共单调定理

Comonotonic theorem for solution of backward doubly stochastic differential equation

首先在比倒向随机微分方程更一般的倒向重随机微分方程中获得了一个新的比较定理。然后,受倒向随机微分方程共单调定律的启发,并利用获得的新的比较定理,首次得到了倒向重随机微分方程解z的共单调定理;其结果推广了许多已有的结果。

First, we obtain a new comparison theorem for backward doubly stochastic differential equation which is more popular than backward differential equation. Then inspired by the comonotomic theorem of backward stochastic differential equation, and by using the new comparison theorem,we obtain comonotonic theorem for solwtion z of backward doubly stochastic differential equation. The results can generalize some existing results.