Hyers-Ulam stability of coupled systems for stochastic differential equations with random impulses driven by Poisson jumps

Yasir A. Madani; Tayeb Blouhi; Fatima Zohra Ladrani; Mohamed Bouye; Khaled Zennir; Keltoum Bouhali; Amin Benaissa Cherif; Yasir A. Madani; Tayeb Blouhi; Fatima Zohra Ladrani; Mohamed Bouye; Khaled Zennir; Keltoum Bouhali; Amin Benaissa Cherif

doi:10.3934/math.20251123

AIMS Mathematics

2025, Volume 10, Issue 11: 25358-25379. doi: 10.3934/math.20251123

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Research article

Hyers-Ulam stability of coupled systems for stochastic differential equations with random impulses driven by Poisson jumps

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 55473, Saudi Arabia
2.
Department of Mathematics, Faculty of Mathematics and Informatics, University of Science and Technology of Oran Mohamed-Boudiaf (USTOMB), El Mnaouar, BP 1505, Bir El Djir, Oran, 31000, Algeria
3.
Department of Exact Sciences, Higher Training Teachers School of Oran Ammour Ahmed (ENSO), Oran, 31000, Algeria
4.
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
5.
Department of Mathematics, College of Science, Qassim University, Saudi Arabia

Received: 10 April 2025 Revised: 23 October 2025 Accepted: 30 October 2025 Published: 05 November 2025
MSC : 34A37, 34F05, 34G20, 47H10, 60H10

The problem of existence, uniqueness, and stability in the Hyers-Ulam sense of solutions for random impulsive stochastic functional differential equations driven by Poisson jumps with finite delays is considered. Based on techniques combining the generalized Banach fixed-point theorem and the expansion of the Perov-type fixed-point theorem, two significant quantitative and qualitative results are analyzed, and then an example is presented to illustrate our results.
- stochastic analysis,
- impulsive differential equations,
- matrix convergent to zero,
- iterative methods,
- Hyers-Ulam stability,
- Wiener process,
- Poisson process
Citation: Yasir A. Madani, Tayeb Blouhi, Fatima Zohra Ladrani, Mohamed Bouye, Khaled Zennir, Keltoum Bouhali, Amin Benaissa Cherif. Hyers-Ulam stability of coupled systems for stochastic differential equations with random impulses driven by Poisson jumps[J]. AIMS Mathematics, 2025, 10(11): 25358-25379. doi: 10.3934/math.20251123

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Abstract

The problem of existence, uniqueness, and stability in the Hyers-Ulam sense of solutions for random impulsive stochastic functional differential equations driven by Poisson jumps with finite delays is considered. Based on techniques combining the generalized Banach fixed-point theorem and the expansion of the Perov-type fixed-point theorem, two significant quantitative and qualitative results are analyzed, and then an example is presented to illustrate our results.

References

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