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Asymptotic analysis of mathematical expectation of the total energy of a harmonic oscillator perturbed by the “shot-noise”-type process

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We study the behavior, as t → ∞, of the mathematical expectation of the total energy of a harmonic oscillator without friction perturbed by the “shot noise”-type process.

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References

  1. L. É. Él’sgol’ts, Differential Equations and Variational Calculus [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  2. H. L. Kulinich, D. Yu. Kurovs’kyi, and D. V. Petrusenko, “Asymptotic analysis of the mathematical expectation of the total energy of a harmonic oscillator under random pulse perturbation,” Nelin. Kolyvannya, 12, No. 3, 299–306 (2009); English translation: Nonlin. Oscillations, 12, No. 3, 305–313 (2009).

    Google Scholar 

  3. M. T. Dyvnych, D. Yu. Kurovs’kyi, and A. V. Ershov, “Asymptotic analysis of the mathematical expectation of the total energy of a random harmonic oscillator,” Visn. Kyiv. Univ., Ser. Mat. Mekh., No. 3, 104–112 (2005).

  4. G. L. Kulinich, “On the limiting behaviors of a harmonic oscillator with random external disturbance,” Y.A. M.S.A., 8, 265–274 (1995).

    MATH  MathSciNet  Google Scholar 

  5. G. M. Fikhtengol’ts, Foundations of Mathematical Analysis [in Russian], Vol. 2, Gostekhteorizdat, Moscow (1956).

    Google Scholar 

  6. A. A. Andronov, A. A. Vitt, and S. É. Khaikin, Theory of Oscillations [in Russian], Fizmatlit, Moscow (1959).

    Google Scholar 

  7. V. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations [in Russian], Naukova Dumka, Kiev (1968).

    Google Scholar 

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Correspondence to O.D. Stetsyuk.

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Translated from Neliniini Kolyvannya, Vol. 16, No. 4, pp. 547–557, October–December, 2014.

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Stetsyuk, O. Asymptotic analysis of mathematical expectation of the total energy of a harmonic oscillator perturbed by the “shot-noise”-type process. J Math Sci 203, 396–408 (2014). https://doi.org/10.1007/s10958-014-2142-2

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  • DOI: https://doi.org/10.1007/s10958-014-2142-2

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