A note on attraction and stability of neutral stochastic delay differential equations with Markovian switching

Abstract

This paper is concerned with neutral stochastic delay differential equations with Markovian switching (NSDDEs-MS). A kind of ψ − function is introduced and some criteria on the attractor for the product of the ψ − function are obtained. By the new criteria, the almost sure stability with the general decay rate of NSDDEs-MS could be examined, including the exponential stability and the polynomial stability. Finally, an example is provided to illustrate the applications of our results clearly.