Comparison principle and stability of Ito stochastic differential delay equations with Poisson jump and Markovian switching

In this paper the comparison principle for the nonlinear Itô stochastic differential delay equations with Poisson jump and Markovian switching is established. 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. Some known results are generalized and improved.