Moment boundedness of linear stochastic delay differential equations with distributed delay

被引：6
作者：
Wang, Zhen [1 ,2 ]
Li, Xiong [1 ]
Lei, Jinzhi [3 ]
机构：
[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China
[2] Hefei Univ Technol, Sch Math, Hefei 230009, Peoples R China
[3] Tsinghua Univ, Zhou Pei Yuan Ctr Appl Math, Beijing 100084, Peoples R China
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2014年 / 124卷 / 01期
关键词：
Stochastic delay differential equation; Distributed delay; Moment boundedness; STABLE MANIFOLD THEOREM; INVARIANT-MANIFOLDS; STABILITY; SYSTEMS; MEMORY;
D O I：
10.1016/j.spa.2013.09.002
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：
This paper studies the moment boundedness of solutions of linear stochastic delay differential equations with distributed delay. For a linear stochastic delay differential equation, the first moment stability is known to be identical to that of the corresponding deterministic delay differential equation. However, boundedness of the second moment is complicated and depends on the stochastic terms. In this paper, the characteristic function of the equation is obtained through techniques of the Laplace transform. From the characteristic equation, sufficient conditions for the second moment to be bounded or unbounded are proposed. (C) 2013 The Authors. Published by Elsevier B.V. All rights reserved.
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页码：586 / 612
页数：27
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