Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 59032, 6 pages
doi:10.1155/JAMSA/2006/59032
Stability of invariant sets of Itô stochastic
differential equations with Markovian switching
Department of Probability and Statistics, School of Mathematics and Information
Sciences, Guangzhou University, Guangzhou, Guangdong 510006, China
Received 16 January 2004; Revised 26 September 2005; Accepted 26 September 2005
Copyright © 2006 Jiaowan Luo. 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
Consider the nonlinear Itô stochastic differential equations
with Markovian switching, some sufficient conditions for the
invariance, stochastic stability, stochastic asymptotic stability,
and instability of invariant sets of the equations are derived.