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Stationary and periodic solutions of the operator Riccati equation under a random perturbation

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Abstract

Sufficient conditions are presented for the existence of stationary and periodic solutions of the operator Riccati equation under a random perturbation.

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References

  1. A. Ya. Dorogovtsev, “On periodic and bounded solutions of the operator Riccati equation,”Ukr. Mat. Zh.,45, No. 2, 239–242 (1993).

    Google Scholar 

  2. A. Ya. Dorogovtsev, “Stochastically periodic solutions of differential equations with operator coefficients,”Ukr. Mat. Zh.,43, No. 4, 489–496 (1991).

    Google Scholar 

  3. A. T. Bharucha-Reid,Random Integral Equations, Academic Press, New York (1972).

    Google Scholar 

  4. M. G. Krein,Lectures in the Theory of Stability of Solutions to the Differential Equations in a Banach Space [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1954).

    Google Scholar 

  5. J. Riordan,Combinatorial Identities, Wiley, New York-London-Sydney (1968).

    Google Scholar 

  6. J. L. Massera and J. J. Schäffer,Linear Differential Equations and Function Spaces, Academic Press, New York-London (1966).

    Google Scholar 

  7. J. Lucas, “Solving algebraic and differential Riccati operator equations,”Linear Algebra Appl.,144, 71–83 (1991).

    Google Scholar 

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 5, pp. 609–615, May, 1993.

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Dorogovtsev, A.Y. Stationary and periodic solutions of the operator Riccati equation under a random perturbation. Ukr Math J 45, 662–670 (1993). https://doi.org/10.1007/BF01058204

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  • DOI: https://doi.org/10.1007/BF01058204

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