ANALYSIS OF THE ASYMPTOTIC BEHAVIOR OF THE SOLUTION TO A LINEAR STOCHASTIC DIFFERENTIAL EQUATION WITH SUBEXPONENTIALLY STABLE MATRIX AND ITS APPLICATION TO A CONTROL PROBLEM

被引：3

作者：

Palamarchuk, E. S. ^{[1
]}

机构：

[1] Russian Acad Sci, Steklov Math Inst, Moscow 119991, Russia

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2018年 / 62卷 / 04期

基金：

俄罗斯科学基金会;

关键词：

strong law of large numbers; linear equation; nonexponential stability; linear-quadratic regulator; OPTIMALITY;

D O I：

10.1137/S0040585X97T988794

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We analyze the asymptotic behavior of the solution to a linear stochastic differential equation with subexponentially stable matrix. A result in the form of the strong law of large numbers is put forward for a pair of processes consisting of a squared norm of the solution and a deterministic function defined as an integral of the squared norm of the diffusion matrix. This result is applied in solving the problem of a linear-quadratic regulator over an infinite time-horizon for one class of undetectable systems.

引用

页码：522 / 533

页数：12

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