Stability analysis for stochastic Volterra-Levin equations with Poisson jumps: Fixed point approach.

This paper is devoted to investigate a class of stochastic Volterra-Levin equations with Poisson jumps. To the best of the authors' knowledge, till now, the stability problem for this class of new systems has not yet been solved since Poisson jumps are considered. The main objective of this paper is to fill the gap. By using the fixed point theory, we first study the existence and uniqueness of the solution as well as the pth moment exponential stability for the considered system. Then based on the well known Borel-Cantelli lemma, we prove that the solution is almost surely pth moment exponentially stable. Our results improve and generalize those given in the previous literature. Finally, two simple examples are provided to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]