Sensitivity to Small Delays of Pathwise Stability for Stochastic Retarded Evolution Equations

被引：2

作者：

Liu, Kai ^{[1
,2
]}

机构：

[1] Tianjin Normal Univ, Coll Math Sci, Tianjin 300387, Peoples R China

[2] Univ Liverpool, Sch Phys Sci, Dept Math Sci, Liverpool L69 7ZL, Merseyside, England

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2018年 / 31卷 / 03期

关键词：

Stability sensitive to small delays; Pathwise exponential stability; Stochastic delay evolution equation; FUNCTIONAL-DIFFERENTIAL EQUATIONS; TIME DELAYS; STABILIZATION;

D O I：

10.1007/s10959-017-0750-8

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：

In this paper, we shall study the almost sure pathwise exponential stability property for a class of stochastic functional differential equations with delays, possibly, in the highest-order derivative terms driven by multiplicative noise. Instead of establishing a moment exponential stability as the first step and then proceeding to investigate the pathwise stability of the system under consideration, we shall develop a direct approach for this problem. As a consequence, we can show that some systems, which are not exponential momently stable, have the exponential stability not sensitive to small delays in the almost sure sense.

引用

页码：1625 / 1646

页数：22