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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

On an extension of the Lyapunov criterion of stability for quasi-linear systems via integral inequalities methods


Author: Nguyen Huu Du
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 70 (2004).
Journal: Theor. Probability and Math. Statist. 70 (2005), 29-40
MSC (2000): Primary 60H10; Secondary 34F05, 93E15
Published electronically: August 5, 2005
MathSciNet review: 2109820
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Abstract | References | Similar Articles | Additional Information

Abstract: In this article, we concern ourselves with a new concept for comparing the stability degree of two dynamical systems. By using the integral inequality method, we give a criterion which allows us to compare the growth rate of two Itô quasi-linear differential equations. It can be viewed as an extension of the Lyapunov criterion to the stochastic case.


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Additional Information

Nguyen Huu Du
Affiliation: Faculty of Mathematics, Mechanics, and Informatics, Vietnam National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam
Email: nhdu2001@yahoo.com

DOI: http://dx.doi.org/10.1090/S0094-9000-05-00628-9
PII: S 0094-9000(05)00628-9
Keywords: Lyapunov exponent, It\^o's stochastic process, Bihari's inequality
Received by editor(s): December 14, 2002
Published electronically: August 5, 2005
Additional Notes: This work was supported by VNCR program # QT 01.01.
Article copyright: © Copyright 2005 American Mathematical Society