Exponential stability of stochastic differential equation with mixed delay
type: Item
instance of: scholarly article
title: Exponential stability of stochastic differential equation with mixed delay
zbMATH Open document ID: 1406.60092
DOI: 10.1155/2014/187037
author: Wenli Zhu
author: Jiexiang Huang
author: Xinfeng Ruan
author: Zhao Zhao
published in: Journal of Applied Mathematics
publication date: 2019-02-01T00:00:00Z
review text: Summary: This paper focuses on a class of stochastic differential equations with mixed delay based on Lyapunov stability theory, Itô formula, stochastic analysis, and inequality technique. A sufficient condition for existence and uniqueness of the adapted solution to such systems is established by employing fixed point theorem. Some sufficient conditions of exponential stability and corollaries for such systems are obtained by using Lyapunov function. By utilizing Doob's martingale inequality and Borel-Cantelli lemma, it is shown that the exponentially stable in the mean square of such systems implies the almost surely exponentially stable. In particular, our theoretical results show that if stochastic differential equation is exponentially stable and the time delay is sufficiently small, then the corresponding stochastic differential equation with mixed delay will remain exponentially stable. Moreover, time delay upper limit is solved by using our theoretical results when the system is exponentially stable, and they are more easily verified and applied in practice.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 34F05
zbMATH DE Number: 7010564
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/187037
OpenAlex ID: W2160727405
Wikidata QID: Q59050152
description: scientific article; zbMATH DE number 7010564