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Abstract and Applied Analysis
Volume 2014, Article ID 292653, 9 pages
http://dx.doi.org/10.1155/2014/292653
Research Article

Lyapunov Techniques for Stochastic Differential Equations Driven by Fractional Brownian Motion

1School of Sciences, South China University of Technology, Guangzhou 510640, China
2School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640, China
3Mechatronics, Embedded Systems and Automation (MESA) Lab, School of Engineering, University of California, Merced, 5200 N Lake Road, Merced, CA 95343, USA

Received 2 November 2013; Revised 12 January 2014; Accepted 26 January 2014; Published 11 March 2014

Academic Editor: Weilin Xiao

Copyright © 2014 Caibin Zeng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Little seems to be known about evaluating the stochastic stability of stochastic differential equations (SDEs) driven by fractional Brownian motion (fBm) via stochastic Lyapunov technique. The objective of this paper is to work with stochastic stability criterions for such systems. By defining a new derivative operator and constructing some suitable stochastic Lyapunov function, we establish some sufficient conditions for two types of stability, that is, stability in probability and moment exponential stability of a class of nonlinear SDEs driven by fBm. We will also give an example to illustrate our theory. Specifically, the obtained results open a possible way to stochastic stabilization and destabilization problem associated with nonlinear SDEs driven by fBm.