Existence and Exponential Stability of a Class of Impulsive Neutral Stochastic Integrodifferential Equations with Poisson Jumps

Abstract

Stochastic differential equations have been investigated as mathematical models to describe the dynamical behavior of real life phenomena. It is essential to take into account the enviromental disturbances as well as the time delay while constructing realistic models in the area of engineering, biology, etc. In this paper by employing the fractional power of operators and semi group theory we obtain some new criteria ensuring the existence and exponential stability of a class of impulsive neutra stochastic integrodierential equations with Poisson jumps. We use xed point strategy to establish some new sufficient conditions that ensure the exponential stability of mild solution in the mean square moment by utilizing an impulsive integral inequality. 

Keywords

• Existence
• Exponential stability
• impulsive system
• stochastic integrodifferential equations
• poisson jumps

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