Inverse-Positive Matrices and Stability Properties of Linear Stochastic Difference Equations with Aftereffect

Arcady Ponosov () and Ramazan I. Kadiev
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Arcady Ponosov: Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, 1432 Aas, Norway
Ramazan I. Kadiev: Dagestan Research Center of the Russian Academy of Sciences & Department of Mathematics, Dagestan State University, Makhachkala 367005, Russia

Mathematics, 2024, vol. 12, issue 17, 1-15

Abstract: This article examines the stability properties of linear stochastic difference equations with delays. For this purpose, a novel approach is used that combines the theory of inverse-positive matrices and the asymptotic methods developed by N.V. Azbelev and his students for deterministic functional differential equations. Several efficient conditions for p -stability and exponential p -stability ( 2 ≤ p < ∞ ) of systems of linear Itô-type difference equations with delays and random coefficients are found. All results are conveniently formulated in terms of the coefficients of the equations. The suggested examples illustrate the feasibility of the approach.

Keywords: stochastic difference equations; inverse-positive matrices; delay effects (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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