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Comparison principle and stability of Itô stochastic differential delay equations with Poisson jump and Markovian switching. (English) Zbl 1082.60054
Summary: 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 \(p\)th mean, asymptotic stability in the \(p\)th mean and the \(p\)th moment exponential stability of such equations. Some known results are generalized and improved.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34K50 Stochastic functional-differential equations
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