一类随机Riccati方程解的存在性

Existence of Solution for a Class of Stochastic Riccati Equations

考虑一类随机Riccati方程解的存在性条件.首先,基于随机Riccati方程自身结构的特点,利用It8公式,构造一个不带限制条件的倒向随机微分方程;其次,在倒向随机微分方程的构造中先使其解满足随机Riccati方程中相应的代数限制条件,再利用二者间的关系给出随机Riccati方程解的存在性条件.

We considered the existence condition of solution for a class of stochastic Riccati equation. Based on the characteristics of the stochastic Riccati equation, we constructed a backward stochastic differential equation without constraints by using It6 formula. The solution of backward stochastic differential equations satisfied the algebraic constraints corresponding stochastic Riccati equation during the construction. Thus we gave the existence condition of the solution of the stochastic Riccati equation by using the relation of them.