Study on the exponential stability of stochastic functional differential equations with random impulses

Dongdong Gao; Maosheng Ye; Dongdong Gao; Maosheng Ye

doi:10.3934/math.20251342

AIMS Mathematics

2025, Volume 10, Issue 12: 30623-30636. doi: 10.3934/math.20251342

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Research article

Study on the exponential stability of stochastic functional differential equations with random impulses

Dongdong Gao ^{1
,
,},
Maosheng Ye ²

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: 10 October 2025 Revised: 10 December 2025 Accepted: 23 December 2025 Published: 26 December 2025
MSC : 34A37, 34D23, 60H10

This paper investigates the pth moment exponential stability of stochastic functional differential equations (SFDEs) with random impulses. By employing the Razumikhin-type method in combination with mathematical induction, we derive an exponential stability criterion for the considered system. In addition, we elucidate the intermediate mechanisms through which impulsive disturbances affect system stability, thereby extending and generalizing existing results in the literature. Finally, two numerical examples are presented to confirm the correctness and validity of the theoretical findings.
- Razumikhin-type condition,
- exponential stability,
- random impulses
Citation: Dongdong Gao, Maosheng Ye. Study on the exponential stability of stochastic functional differential equations with random impulses[J]. AIMS Mathematics, 2025, 10(12): 30623-30636. doi: 10.3934/math.20251342

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Abstract

This paper investigates the pth moment exponential stability of stochastic functional differential equations (SFDEs) with random impulses. By employing the Razumikhin-type method in combination with mathematical induction, we derive an exponential stability criterion for the considered system. In addition, we elucidate the intermediate mechanisms through which impulsive disturbances affect system stability, thereby extending and generalizing existing results in the literature. Finally, two numerical examples are presented to confirm the correctness and validity of the theoretical findings.

References

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