Exploration on the existence and exponential stability results for second-order impulsive stochastic differential equations with delays

This paper is devoted to investigating the existence and exponential stability of mild solutions for second-order impulsive stochastic differential equations(ISDEs) with delays. First of all, we prove the existence of mild solutions to the considered ISDEs by using the successive approximation method. After that, based on the impulsive differential equation theory and comparison principle, we establish a new impulsive integral inequality, which can effectively improve some known existing results. Furthermore, by resorting to this novel inequality and the stochastic analysis techniques, exponential stability in the pth moment of mild solutions for the considered ISDEs is derived. Finally, the correctness of the theoretical results is verified through an abstract example.