Mean square asymptotic stability in nonlinear stochastic neutral Volterra-Levin equations with Poisson jumps and variable delays

Abstract

In this paper, we use the contraction mapping principle to obtain mean square asymptotic stability results of a nonlinear stochastic neutral Volterra-Levin equation with Poisson jumps and variable delays. An asymptotic stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some previous results due to Burton [5], Becker and Burton [4] and Jin and Luo [10], Ardjouni and Djoudi [1]. Finally, an illustrative example is given.