| 一类随机Riccati方程解的存在性 |
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| 引用本文： | 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(3):613-616. |
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| 作者姓名： | 许洁 吕显瑞 |
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| 作者单位： | 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 |
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| 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.
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| 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 |
| 收稿时间： | 2016-10-17 |
Existence of Solution for a Class of Stochastic Riccati Equations |
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| XU Jie,LV Xianrui.Existence of Solution for a Class of Stochastic Riccati Equations[J].Journal of Jilin University: Sci Ed,2017,55(3):613-616. |
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| Authors: | XU Jie LV Xianrui |
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| Institution: | 1. College of Sciences, Jilin Institute of Chemical Technology, Jilin 132022, Jilin Province, China;2. College of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | We considered the existence condition of solution for aclass 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. |
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| Keywords: | backward stochastic differential equation constraint condition stochastic Riccati equation stochastic linear quadratic optimal control |
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