Exponential Stability of Stochastic Differential Equation with Mixed Delay
Joint Authors
Zhao, Zhao
Zhu, Wenli
Huang, Jiexiang
Ruan, Xinfeng
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-03-04
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Zhu, Wenli& Huang, Jiexiang& Ruan, Xinfeng& Zhao, Zhao. 2014. Exponential Stability of Stochastic Differential Equation with Mixed Delay. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-11.
https://search.emarefa.net/detail/BIM-452943
Modern Language Association (MLA)
Zhu, Wenli…[et al.]. Exponential Stability of Stochastic Differential Equation with Mixed Delay. Journal of Applied Mathematics No. 2014 (2014), pp.1-11.
https://search.emarefa.net/detail/BIM-452943
American Medical Association (AMA)
Zhu, Wenli& Huang, Jiexiang& Ruan, Xinfeng& Zhao, Zhao. Exponential Stability of Stochastic Differential Equation with Mixed Delay. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-11.
https://search.emarefa.net/detail/BIM-452943
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-452943