Exponential stability of impulsive neutral stochastic integrodifferential equations driven by a poisson jumps and time-varying delays

Abstract

The purpose of this work is to study the impulsive neutral stochastic integrodifferential equations driven by a Poisson jumps and time-varying delays. We use the theory of resolvent operators developed in Grimmer the prove an existence, uniqueness and we establish some conditions ensuring the exponential decay to zero in mean square for the mild solution by means of the Banach fixed point theory. Finally, an illustrative example is given to demonstrate the effectiveness of the results.