The pth Moment Stability with General Decay Rate of the Solutions for a Class of Neutral Stochastic Functional Differential Equations
In this paper,the stability of the solutions for a class of neutral stochastic functional differential equations with Markovian switching and Lévy noise is investi-gated.First,an auxiliary functional differential equation is constructed.Then,under some suitable assumptions two sufficient conditions for the pth moment of the so-lutions for the neutral stochastic functional differential equations to be stable with general decay rate are obtained by means of the formula for the variation of param-eters of the auxiliary functional differential equation,some inequality technique and comparison principle.The obtained results generalize the results in some earlier pub-lications.Finally,two examples and numerical simulations are given to illustrate the effectiveness of the results.
Stochastic functional differential equationgeneral decay rateMarko-vian switchingLévy noiseItô formula
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