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Stability of solutions of systems of linear Itô difference equations with aftereffect with respect to the initial data

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Abstract

We study the p-stability (2 ≤ p < ∞) of the trivial solution for homogeneous systems of linear Itô difference equations with aftereffect with respect to the initial data. We obtain sufficient conditions for the stability of specific systems in terms of parameters of these systems. The study is carried out by the method of auxiliary (or model) equations.

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References

  1. Kadiev, R. and Ponosov, A., The W-Transform in Stability Analysis for Stochastic Linear Functional Difference Equations, J. Math. Anal. Appl., 2012, vol. 389, no. 2, pp. 1239–1250.

    Article  MATH  MathSciNet  Google Scholar 

  2. Kadiev, R. and Ponosov, A., Exponential Stability of Itô-Type Linear Functional Difference Equations, Comput. Math. Appl., 2013, vol. 66, no. 11, pp. 2295–2306.

    Article  MathSciNet  Google Scholar 

  3. Kadiev, R.I., Stability of Solutions of Linear Itô Functional-Differential Equations and N.V. Azbelev W-Method, Vestn. Tambov. Univ. Estestv. Tekhn. Nauki, 2013, vol. 18, no. 5, pp. 2543–2545.

    MATH  Google Scholar 

  4. Kadiev, R.I. and Shakhbanova, Z.I., Stability of Solutions of Linear Itô Functional-Difference Equations with Respect to the Initial Data, Vestn. Dagestan. Univ. Estestv. Nauki, 2012, vol. 6, pp. 141–146.

    Google Scholar 

  5. Azbelev, N.V., Maksimov, V.P., and Rakhmatullina, L.F., Vvedenie v teoriyu funktsional’no-differentsial’nykh uravnenii (Introduction to the Theory of Functional-Differential Equations), Moscow Nauka, 1991.

    Google Scholar 

  6. Berezansky, L. and Braverman, E., On Exponential Dichotomy, Bohl Perron Type Theorems and Stability of Difference Equations, J. Math. Anal. Appl., 2005, no. 304, pp. 511–530.

    Article  MATH  MathSciNet  Google Scholar 

  7. Braverman, E. and Karabach, I.M., Bohl-Perron-Type Stability Theorems for Linear Difference Equations with Infinite Delay, J. Difference Equ. Appl., 2012, vol. 5, no. 5, pp. 909–939.

    Article  Google Scholar 

  8. Kadiev, R.I., Sufficient Conditions for the Stability of Stochastic Systems with Aftereffect, Differ. Uravn., 1994, vol. 30, no. 2, pp. 555–564.

    MathSciNet  Google Scholar 

  9. Kadiev, R.I. and Panosov, A.V., Stability of Linear Stochastic Functional-Differential Equations with Constantly Acting Perturbations, Differ. Uravn., 1992, vol. 28, no. 2, pp. 198–207.

    MATH  Google Scholar 

  10. Kadiev, R.I. and Ponosov, A.V., Relations between Stability and Admissibility for Stochastic Linear Functional Differential Equations, J. Funct. Differ. Equat., 2004, pp. 1–28.

    Google Scholar 

  11. Liptser, R. Sh. and Shiryaev, F.N., Teoriya martingalov (Theory of Martingales), Moscow, 1986. DIFFERENTIAL EQUATIONS

    Google Scholar 

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Authors and Affiliations

  1. Dagestan State University, Makhachkala, Russia

    R. I. Kadiev

  2. Dagestan Scientific Center, Russian Academy of Sciences, Makhachkala, Russia

    R. I. Kadiev

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  1. R. I. Kadiev
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Correspondence to R. I. Kadiev.

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Original Russian Text © R.I. Kadiev, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 7, pp. 842–850.

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Kadiev, R.I. Stability of solutions of systems of linear Itô difference equations with aftereffect with respect to the initial data. Diff Equat 51, 838–846 (2015). https://doi.org/10.1134/S0012266115070022

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  • DOI: https://doi.org/10.1134/S0012266115070022

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