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Limiting behavior of an oscillatory system in the presence of random perturbations of the parameters of this system. II

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Abstract

The asymptotic behavior is studied of the solution of a second-order linear system in the presence of random perturbations represented by an ergodic Markov process with a finite state space. The case is investigated when the averaged system describes a simple harmonic oscillation.

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Literature cited

  1. I. V. Skorokhod, “The limiting behavior of an oscillatory system in the presence of random perturbations of the parameters of this system. I,” Ukr. Mat. Zh.,41, No. 10, 1357–1364 (1989).

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  2. I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations and Their Applications [in Russian], Naukova Dumka, Kiev (1982).

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  3. A. V. Skorokhod, Asymptotic Methods of the Theory of Stochastic Differential Equations [in Russian], Naukova Dumka, Kiev (1987).

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Authors and Affiliations

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

    I. V. Skorokhod

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  1. I. V. Skorokhod
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 6, pp. 817–820, June, 1990.

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Skorokhod, I.V. Limiting behavior of an oscillatory system in the presence of random perturbations of the parameters of this system. II. Ukr Math J 42, 721–724 (1990). https://doi.org/10.1007/BF01058921

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  • DOI: https://doi.org/10.1007/BF01058921

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