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Fluctuations of a stochastic system under an asymptotic diffusive perturbation

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Abstract

A stochastic singularly perturbed system is considered. Sufficient conditions of the asymptotic normality are obtained for the dynamic system in the vicinity of its equilibrium point. To this end, a solution to the singular perturbation problem is constructed for an asymptotic representation of the generator of a Markov renewal process.

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References

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Authors and Affiliations

  1. Institute of Applied Mathematics and Fundamental Sciences of National University “Lvivs’ka Politekhnika”, Lvov, Ukraine

    S. A. Semenyuk & Ya. M. Chabanyuk

Authors
  1. S. A. Semenyuk
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  2. Ya. M. Chabanyuk
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Correspondence to S. A. Semenyuk.

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Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 104–109, September–October 2008.

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Semenyuk, S.A., Chabanyuk, Y.M. Fluctuations of a stochastic system under an asymptotic diffusive perturbation. Cybern Syst Anal 44, 716–721 (2008). https://doi.org/10.1007/s10559-008-9042-8

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  • DOI: https://doi.org/10.1007/s10559-008-9042-8

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