Stability analysis of neutral stochastic differential delay equations driven by Lévy noises

Abstract

This paper mainly analyzes the well-posedness, and the stability analysis for the global solution of neutral stochastic differential delay equations (NSDDEs) driven by Lévy noises. By using an integral lemma and a Lyapunov function approach, the existence and uniqueness theorem is proved. Then, by using the inequality technique and the stochastic analysis theory, the exponential stability in pth(p ≥ 2) moment of such equations is discussed. By using another integral lemma, and using the Baralat lemma as well as the stochastic analysis, the almost surely asymptotic stability is also studied. Finally, one example is given to check the effectiveness of the findings derived.