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

Dongdong Gao; Daipeng Kuang; Jianli Li; Dongdong Gao; Daipeng Kuang; Jianli Li

doi:10.3934/math.2023780

AIMS Mathematics

2023, Volume 8, Issue 7: 15269-15284. doi: 10.3934/math.2023780

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Research article

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

1.
Department of Mathematics and Computer Science, Tongling University, Tongling, Anhui 244000, China
2.
College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, China

Received: 13 February 2023 Revised: 03 April 2023 Accepted: 07 April 2023 Published: 25 April 2023
MSC : 34K20, 60H15, 60J75

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 $ p $th 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.
- existence,
- uniqueness,
- impulsive-integral inequality,
- Poisson jumps,
- exponential stability in the $ p $th moment
Citation: Dongdong Gao, Daipeng Kuang, Jianli Li. Some results on the existence and stability of impulsive delayed stochastic differential equations with Poisson jumps[J]. AIMS Mathematics, 2023, 8(7): 15269-15284. doi: 10.3934/math.2023780

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Abstract

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 $ p $th 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.

References

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