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STABILITY OF HALF-LINEAR NEUTRAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH DELAYS

Part of: Functional-differential and differential-difference equations

Published online by Cambridge University Press:  13 August 2009

MENG WU ,
NAN-JING HUANG  and
CHANG-WEN ZHAO
MENG WU
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, PR China (email: [email protected])
NAN-JING HUANG*
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, PR China (email: [email protected])
CHANG-WEN ZHAO
Affiliation:
College of Business & Management, Sichuan University, Chengdu, Sichuan 610064, PR China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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In this paper, we study the mean square asymptotic stability of a generalized half-linear neutral stochastic differential equation with variable delays applying fixed point theory. An asymptotic mean square stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some results due to Burton, Zhang and Luo. Two examples are given to illustrate our results.

Keywords

fixed pointsstabilityneutral stochastic differential equationsvariable delays

MSC classification

Secondary: 34K50: Stochastic functional-differential equations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 3 , December 2009 , pp. 369 - 383
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

Footnotes

This work was supported by the National Natural Science Foundation of China (10671135, 70831005) and Specialized Research Fund for the Doctoral Program of Higher Education (20060610005).

References

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