Some results on the existence and stability of impulsive delayed stochastic differential equations with Poisson jumps

This paper is concerned with the existence, uniqueness and exponential stability of mild solutions for a class of impulsive stochastic differential equations driven by Poisson jumps and time - varying delays. Utilizing the successive approximation method, we obtain the criteria of existence and uniqueness of mild solutions for the considered impulsive stochastic differential equations. Then, the exponential stability in the pth moment of the mild solution is also devised for considered equations by establishing an improved impulsive-integral inequality, which improves some known existing ones. Finally, an example and numerical simulations are given to illustrate the efficiency of the obtained theoretical results.

Automated summary

This paper focuses on the existence, uniqueness, and exponential stability of mild solutions for impulsive stochastic differential equations with Poisson jumps and time-varying delays. By utilizing the successive approximation method, the criteria for the existence and uniqueness of mild solutions are obtained. An improved impulsive-integral inequality is established to prove the exponential stability in the pth moment of the mild solution, which improves existing results. An example and numerical simulations are provided to demonstrate the effectiveness of the theoretical findings.