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Criteria of the mean-square asymptotic stability of solutions of systems of linear stochastic difference equations with continuous time and delay

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Abstract

We obtain spectral and algebraic coefficient criteria and sufficient conditions for the mean-square asymptotic stability of solutions of systems of linear stochastic difference equations with continuous time and delay. We consider the case of a rational correlation between delays and a “white-noise”-type stochastic perturbation of coefficients. We use the method of Lyapunov functions. Most results are presented in terms of the Sylvester and Lyapunov matrix algebraic equations.

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References

  1. D. G. Korenevskii, “On the asymptotic stability of solutions of systems of deterministic and stochastic linear stationary difference equations with delay,” Dokl. Akad Nauk SSSR, 322, No. 2, 219–223 (1992).

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    D. G. Korenevskii

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  1. D. G. Korenevskii
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 8, pp. 1073–1081, August, 1998.

This work was partially supported by the Joint Foundation of the Ukrainian Government and the Soros International Science Foundation (grant No. K42100).

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Korenevskii, D.G. Criteria of the mean-square asymptotic stability of solutions of systems of linear stochastic difference equations with continuous time and delay. Ukr Math J 50, 1224–1232 (1998). https://doi.org/10.1007/BF02513094

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  • DOI: https://doi.org/10.1007/BF02513094

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