一类随机Riccati方程解的存在性

吉林大学学报(理学版)

一类随机Riccati方程解的存在性

许洁^1,2, 吕显瑞^2

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

收稿日期:2016-10-17 出版日期:2017-05-26 发布日期:2017-05-31
通讯作者: 吕显瑞 E-mail:lvxr@jlu.edu.cn

Existence of Solution for a Class of Stochastic Riccati Equations

XU Jie^1,2, LV Xianrui²

1. College of Sciences, Jilin Institute of Chemical Technology, Jilin 132022, Jilin Province, China;2. College of Mathematics, Jilin University, Changchun 130012, China

Received:2016-10-17 Online:2017-05-26 Published:2017-05-31
Contact: LV Xianrui E-mail:lvxr@jlu.edu.cn

摘要/Abstract

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It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.

关键词: 随机线性二次最优控制, 倒向随机微分方程, 限制条件, 随机Riccati方程

Abstract: 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 It 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.

Key words: backward stochastic differential equation, constraint condition, stochastic Riccati equation, stochastic linear quadratic optimal control

中图分类号:

O211.63

许洁, 吕显瑞. 一类随机Riccati方程解的存在性[J]. 吉林大学学报(理学版), 2017, 55(03): 613-616.

XU Jie, LV Xianrui. Existence of Solution for a Class of Stochastic Riccati Equations[J]. Journal of Jilin University Science Edition, 2017, 55(03): 613-616.