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Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 206438, 20 pages
http://dx.doi.org/10.1155/2012/206438
Research Article

Stochastic Functional Differential Equation under Regime Switching

Institute of Mathematics Science, Jilin University, Changchun 130012, China

Received 6 April 2012; Revised 24 June 2012; Accepted 4 July 2012

Academic Editor: Victor S. Kozyakin

Copyright © 2012 Ling Bai and Zhang Kai. 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

We discuss stochastic functional differential equation under regime switching . We obtain unique global solution of this system without the linear growth condition; furthermore, we prove its asymptotic ultimate boundedness. Using the ergodic property of the Markov chain, we give the sufficient condition of almost surely exponentially stable of this system.