Stability analysis of stochastic delay differential equations with Lévy noise

Abstract

This paper is concerned with pth moment exponential stability problem for a class of stochastic delay differential equations driven by Lévy processes. Several new stability theorems are obtained by developing a method—proof by contradiction. Moreover, the results are applied to investigate the pth moment exponential stability of stochastic neural networks with Lévy noise. In particular, the time-varying delay in our results is not required to be differentiable, even not continuous. The obtained results improve greatly some previous works given in the literature. In particular, our method can easily correct the incorrect proofs appeared in two recent papers. Finally, two examples are provided to show the effectiveness of the theoretical results.