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

Author

Listed:
  • Arcady Ponosov

    (Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, 1432 Aas, Norway
    These authors contributed equally to this work.)

  • Ramazan I. Kadiev

    (Dagestan Research Center of the Russian Academy of Sciences & Department of Mathematics, Dagestan State University, Makhachkala 367005, Russia
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Arcady Ponosov & Ramazan I. Kadiev, 2024. "Inverse-Positive Matrices and Stability Properties of Linear Stochastic Difference Equations with Aftereffect," Mathematics, MDPI, vol. 12(17), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2710-:d:1468022
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