广义逆与向后随机微分方程的弱解

Generalized Inverse and the Weak Solution for BSDE

设（Ω，Ｆ，Ｐ）是一个概率空间，Ａ为定义在其上的随机矩阵，引入随机广义逆矩阵以及Ｆｔ－循序可测性的概念，并利用它们来讨论向后随机微分方程ｄＸｔ＝－ｇ（ｔ，Ｘｔ，Ｙｔ）ｄｔ＋ＹｔｄｔＸＴ＝ζ｛（１）的解．其中ζ∈Ｌ２（Ω，Ｆ，Ｐ），ｇ：Ｒ×Ｒｎ×Ｒｎｄ→Ｒｎ（有界可测函数）

Suppose (Ω,F,P) be a probbility space, A is a matrix with every element to be a stochastic process defined on it . We introduce the conception of generalized random inverse matrix and F progressivly measurable matrix. With the help of generalized random inverse, we discussed the stochastic differential equation