Stochastic Functional Differential Equations with Markovian Switching

Abstract

The main aim of this paper is to investigate the exponential stability of stochastic functional differential equations with Markovian switching. The Razumikhin argument and the generalized Ito formula will play an important role in this paper. Applying our new results to several important types of equations e.g. stochastic differential delay equations and stochastic differential equations, both with Markovian switching, we obtain a number of very useful results. Several examples are also given for illustration.