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Approximate solution of the Fokker-Planck-Kolmogorov equation

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Ukrainian Mathematical Journal Aims and scope

Abstract

For the Fokker-Planck-Kolmogorov equation, the higher approximations are constructed by using the Bogolyubov averaging method.

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References

  1. N. N. Bogolyubov and Yu. A. Mitropol'skii,Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1974).

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  2. R. Z. Khas'minskii, “On the averaging principle for parabolic and elliptic differential equations and Markovian processes with small diffusion,”Teor. Veroyatn. Primen.,8, Issue 1, 9–25 (1963).

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

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  4. Yu. A. Mitropol'skii, Nguen Van Dao, and Nguen Dong An',Nonlinear Oscillations in Systems of Arbitrary Order [in Russian], Naukova Dumka, Kiev (1992).

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Authors and Affiliations

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

    Yu. A. Mitropol'skii (Academician)

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  1. Yu. A. Mitropol'skii
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 3, pp. 351–361, March, 1995.

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Mitropol'skii, Y.A. Approximate solution of the Fokker-Planck-Kolmogorov equation. Ukr Math J 47, 408–419 (1995). https://doi.org/10.1007/BF01056303

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  • DOI: https://doi.org/10.1007/BF01056303

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