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Research Article | Open Access

About one unsolved problem in asymptotic p-stability of stochastic systems with delay

Department of Mathematics, Ariel University, Ariel 40700, Israel
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Abstract

The problem of asymptotic p-stability for a linear differential equation with delay and stochastic perturbations, described by a set of mutually independent standard Wiener processes and the Poisson measure, is considered. It is shown the solution of this stability problem for some particular cases of the considered stochastic delay differential equation. However, for the general case of the considered equation, the proposed problem remains open and is presented to the attention of potential readers.

Keywords

stochastic perturbationswhite noisePoisson's jumpsasymptotic p-stabilitystability in probabilitygeneral method of Lyapunov functionals construction
CLC number: Primary: 34F05, 34K20, 37J25; Secondary: 60G52, 65C30

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AIMS Mathematics
Volume 9 Issue 11,
November 2024
Pages 32571-32577
DOI: 10.3934/math.20241560

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Cite this article:
Shaikhet L. About one unsolved problem in asymptotic p-stability of stochastic systems with delay. AIMS Mathematics, 2024, 9(11): 32571-32577. https://doi.org/10.3934/math.20241560

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Received: 09 September 2024
Revised: 30 October 2024
Accepted: 12 November 2024
Published: 18 November 2024
©2024 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)