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Asymptotic behavior of solutions of stochastic recurrence equations in Rd

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Ukrainian Mathematical Journal Aims and scope

Abstract

We study convergence to zero and boundedness with probability one of solutions of stochastic recurrence equations under matrix norms.

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Literature cited

  1. V. A. Koval', “Comparison theorems for multidimensional Gaussian Markov and Gaussian m-Markov sequences,” in: Stochastic Systems and Their Applications [in Russian], Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, Kiev (1990), pp. 60–65.

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  2. V. V. Voevodin and Yu. A. Kuznetsov, Matrices and Computations [in Russian], Nauka, Moscow (1984).

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  3. V. V. Buldygin and S. A. Solntsev, Functional Methods in Problems of Sums of Random: Variables [in Russian], Naukova Dumka, Kiev (1989).

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Authors and Affiliations

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

    V. A. Koval'

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  1. V. A. Koval'
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 6, pp. 829–833, 1991.

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Koval', V.A. Asymptotic behavior of solutions of stochastic recurrence equations in Rd . Ukr Math J 43, 776–779 (1991). https://doi.org/10.1007/BF01058946

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  • DOI: https://doi.org/10.1007/BF01058946

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