Comparison principle and stability criteria for stochastic differential delay equations with Markovian switching

Abstract

In the present paper we first obtain the comparison principle for the nonlinear stochastic differential delay equations with Markovian switching. Later, using this comparison principle, we obtain some stability criteria, including stability in probability, asymptotic stability in probability, stability in the pth mean, asymptotic stability in the pth mean and the pth moment exponential stability of such equations. Finally, an example is given to illustrate the effectiveness of our results.