一类随机Riccati方程解的存在性  

Existence of Solution for a Class of Stochastic Riccati Equations

作　　者：许洁[1,2] 吕显瑞[2] 

机构地区：[1]吉林化工学院理学院,吉林吉林132022 [2]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2017年第3期613-616,共4页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11371169);中国汽车产业创新发展联合基金(批准号:U1564213);大庆师范学院博士启动基金(批准号:12zr09)

摘　　要：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.

关 键 词：随机Riccati方程 限制条件 倒向随机微分方程 随机线性二次最优控制 

分 类 号：O211.63[理学—概率论与数理统计]