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Research Article | Open Access

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

Yasir A. Madani1, Tayeb Blouhi2, Fatima Zohra Ladrani3, Mohamed Bouye4, Khaled Zennir5( ), Keltoum Bouhali5, Amin Benaissa Cherif2
Department of Mathematics, College of Science, University of Ha'il, Ha'il 55473, Saudi Arabia
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
Department of Exact Sciences, Higher Training Teachers School of Oran Ammour Ahmed (ENSO), Oran, 31000, Algeria
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
Department of Mathematics, College of Science, Qassim University, Saudi Arabia
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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.

Keywords

stochastic analysisimpulsive differential equationsmatrix convergent to zeroiterative methodsHyers-Ulam stabilityWiener processPoisson process
CLC number: 34A37, 34F05, 34G20, 47H10, 60H10

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AIMS Mathematics
Volume 10 Issue 11,
November 2025
Pages 25358-25379
DOI: 10.3934/math.20251123

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Cite this article:
Madani YA, Blouhi T, Ladrani FZ, et al. Hyers-Ulam stability of coupled systems for stochastic differential equations with random impulses driven by Poisson jumps. AIMS Mathematics, 2025, 10(11): 25358-25379. https://doi.org/10.3934/math.20251123

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Received: 10 April 2025
Revised: 23 October 2025
Accepted: 30 October 2025
Published: 05 November 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)