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Exponential stability of neutral stochastic delay differential equations with Poisson jumps. (English) Zbl 1240.60158

Summary: The existence and the exponential stability of unique global solutions for the neutral stochastic delay differential equations with Poisson jumps (NSDDEswPJs) are concerned in this paper. By applying the Lyapunov function method and the stochastic analysis theory, a criterion on exponential stability of NSDDEswPJs is discussed. The criterion not only covers many highly non-linear NSDDEswPJs with variable time delay, but also can be verified much more easily than the known criteria.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34K50 Stochastic functional-differential equations
34F05 Ordinary differential equations and systems with randomness
34K20 Stability theory of functional-differential equations
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