超前倒向重随机微分方程

Anticipated backward doubly stochastic diferential equations

本文研究一类带Lipschitz系数的超前倒向重随机微分方程.首先利用压缩映像原理得到这类方程的解的存在唯一性,然后给出一维情形下几种不同形式的比较定理,并给出大量的例子来展示所得理论结果的应用.

This paper studies one kind of anticipated backward doubly stochastic diferential equations with Lipschitz coefcients. Firstly we obtain the existence and uniqueness result of the solution by contraction mapping principle, and then present several comparison theorems in the one-dimensional case. Many examples are given to show the applications of the theoretical results.