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Bounded and periodic solutions of a difference equation and its stochastic analogue in Banach space

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Ukrainian Mathematical Journal Aims and scope

Abstract

Theorems are proved on the existence and uniqueness of bounded and periodic solutions of a linear difference equation with operator coefficients in Banach space. For the stochastic analogue of the investigated equation, the existence and uniqueness are proved of solutions of a special form, periodic and stationary in the narrow sense.

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Literature cited

  1. A. Ya. Dorogovtsev, “Stationary and periodic solutions of a stochastic difference equation in a Banach space,” Teor. Veroyat. Mat. Statist.,42, 35–42 (1990).

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  2. L. A. Lyusternik and V. I. Sobolev, A Short Course in Functional Analysis [in Russian], Vyssh. Shk., Moscow (1982).

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  3. M. F. Gorodnii and A. Ya. Dorogovtsev, “Stationary solutions of a stochastic two-dimensional difference equation in Banach space,” in: Stochastic Analysis and Its Applications [in Russian], Mathematics Institute, Academy of Sciences of the Ukrainian SSR, Kiev (1989), pp. 25–33.

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Authors and Affiliations

  1. Kiev University, USSR

    M. F. Gorodnii

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  1. M. F. Gorodnii
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 1, pp. 41–46, January, 1991.

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Gorodnii, M.F. Bounded and periodic solutions of a difference equation and its stochastic analogue in Banach space. Ukr Math J 43, 32–37 (1991). https://doi.org/10.1007/BF01066900

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  • DOI: https://doi.org/10.1007/BF01066900

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