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Matrix algebraic criteria and sufficient conditions for asymptotic stability and boundedness with probability 1 of the solutions of a system of linear stationary integrodifferential stochastic Ito equations

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Literature cited

  1. D. G. Korenevskii, “A coefficient algebraic criterion for the asymptotic stability with probability 1 of solutions of linear systems of stochastic Ito equations,” in: Numerical Analytic Methods of Studying the Dynamics and Stability of Complex Systems [in Russian], Inst. Mat. Akad. Nauk Ukr.SSR, Kiev (1984), pp.67–77.

    Google Scholar 

  2. I. A. Rudomino-Dusyatskaya, “The mean-square stability of solutions of stochastic differential equations,” Ukr. NIINTI No. 507 Uk-D83 (1983).

  3. I. A. Rudomino-Dusyatskaya, “Asymptotic properties of systems of linear stochastic differential equations,” Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Kiev (1984).

    Google Scholar 

  4. P. V. Pakshin, “The stability of linear and special nonlinear stochastic systems with parametric noise,” in: The Dynamics of Nonhomogeneous Systems, Seminar Notes [in Russian], VNII Systems Research, Moscow (1983), pp. 26–40.

    Google Scholar 

  5. B. I. Rabinovich, Introduction to the Dynamics of Rocket-propelled Spacecraft [in Russian], Mashinostroenie, Moscow (1975).

    Google Scholar 

  6. S. M. Belotserkovskii, Yu. A. Kochetkov, A. A. Krasovskii,and V. V. Novitskii, Introduction to Aeroelasticity [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  7. S. M. Belotserkovskii (ed.), The Creation and Application of Mathematical Models of Aircraft [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  8. I. S. Astapov, S. M. Belotserkovskii, B. O. Kachanov, and Yu. A. Kochetkov, “On systems of integrodifferential equations describing irregular motion of bodies in a continuous medium,” Diff. Uravn.,18, No. 9, 1628–1637 (1982).

    Google Scholar 

  9. B. I. Rabinovich, Applied Problems of Stability of Stabilized Objects [in Russian], Mashinostroenie, Moscow (1978).

    Google Scholar 

  10. E. V. Shakhanova, “An integrodifferential equation in the theory of electron bundles,” in: Functional Analysis and Its Applications in Mechanics and the Theory of Probability [in Russian], Moscow State Univ. (1984), pp. 108–113.

  11. R. K. Miller, “Asymptotic stability properties of linear Volterra integrodifferential equations,” J. Different. Equat.,10, No. 2, 485–506 (1971).

    Google Scholar 

  12. D. L. Abrahamson and E. F. Infante, “A Lyapunov functional for linear Volterra integrodifferential equations,” Qt. Appl. Math.,41, No. 1, 35–44 (1983).

    Google Scholar 

  13. T. A. Burton, “Construction of Lyapunov functionals for Volterra equations,” J. Math. Anal. Appl.,85, No. 1, 90–105 (1982).

    Google Scholar 

  14. T. A. Burton, “Perturbed Volterra equations,” J. Different. Equat.,43, No. 2, 168–183 (1982).

    Google Scholar 

  15. I. I. Gikhman, “On the stability of solutions of stochastic differential equations,” in: Limit Theorems and Statistical Deduction [in Russian], FAN, Tashkent (1966), pp. 14–45.

    Google Scholar 

  16. G. J. Kushner, Stochastic Stability and Control [Russian translation], Mir, Moscow (1969).

    Google Scholar 

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Authors and Affiliations

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

    D. G. Korenevskii

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  1. D. G. Korenevskii
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 38, No. 6, pp. 723–728, November–December, 1986.

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Korenevskii, D.G. Matrix algebraic criteria and sufficient conditions for asymptotic stability and boundedness with probability 1 of the solutions of a system of linear stationary integrodifferential stochastic Ito equations. Ukr Math J 38, 607–612 (1986). https://doi.org/10.1007/BF01056644

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  • DOI: https://doi.org/10.1007/BF01056644

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