Asymptotic Behavior Analysis for Stochastic Integro-Differential Equations with Impulses and Poisson Jump

In this work, we investigate the existence and asymptotic stability in mean square of mild solutions for non-linear impulsive neutral stochastic evolution equations with infinite delays in distribution in a real separable Hilbert space. By using the Banach fixed point principle, some suffcient conditions are derived to ensure the asymptotic stability of mild solutions. Moreover, we investigate the Hyers-Ulam stability for such stochastic system. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained results.