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Volume 15
Issue 6
10.3390/axioms15060439
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Article

About a Problem of Stabilization by Noise for a System of Linear Differential Equations

by
Leonid Shaikhet
Department of Mathematics, Ariel University, Ariel 40700, Israel
Axioms 2026, 15(6), 439; https://doi.org/10.3390/axioms15060439 (registering DOI)
Submission received: 28 April 2026 / Revised: 5 June 2026 / Accepted: 9 June 2026 / Published: 12 June 2026
(This article belongs to the Section Mathematical Analysis)
Versions Notes

Abstract

The well-known effect of stabilization by noise for Ito’s scalar linear stochastic differential equation was proven by R.Z. Khasminskii more than 50 years ago. Here, a similar statement is obtained for a system of linear stochastic differential equations. The obtained result is illustrated on the system of two linear stochastic differential equations via several special examples with numerical simulations and figures.
Keywords: Wiener processes; stochastic perturbations; stability in probability; numerical simulations; trajectories converge to zero Wiener processes; stochastic perturbations; stability in probability; numerical simulations; trajectories converge to zero

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MDPI and ACS Style

Shaikhet, L. About a Problem of Stabilization by Noise for a System of Linear Differential Equations. Axioms 2026, 15, 439. https://doi.org/10.3390/axioms15060439

AMA Style

Shaikhet L. About a Problem of Stabilization by Noise for a System of Linear Differential Equations. Axioms. 2026; 15(6):439. https://doi.org/10.3390/axioms15060439

Chicago/Turabian Style

Shaikhet, Leonid. 2026. "About a Problem of Stabilization by Noise for a System of Linear Differential Equations" Axioms 15, no. 6: 439. https://doi.org/10.3390/axioms15060439

APA Style

Shaikhet, L. (2026). About a Problem of Stabilization by Noise for a System of Linear Differential Equations. Axioms, 15(6), 439. https://doi.org/10.3390/axioms15060439

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