About asymptotic behavior of the mathematical expectation of the total energy of the harmonic oscillator with random perturbation
Тип публікації :
Стаття
Дата випуску :
2018
Автор(и) :
Zimin, O. I.
Kulinich, G. L.
Мова основного тексту :
Англійська
eKNUTSHIR URL :
Випуск :
3
ISSN :
1812-5409
Початкова сторінка :
47
Кінцева сторінка :
52
Цитування :
[APA 7] Zimin, O. I., & Kulinich, G. L. (2018). About asymptotic behavior of the mathematical expectation of the total energy of the harmonic oscillator with random perturbation. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (3), 47–52. https://doi.org/10.17721/1812-5409.2018/3.6
[ДСТУ] Zimin O. I., Kulinich G. L. About asymptotic behavior of the mathematical expectation of the total energy of the harmonic oscillator with random perturbation. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics. 2018. no. 3. P. 47—52. DOI: 10.17721/1812-5409.2018/3.6 (date of access: 18.07.2026).
In this article, the asymptotic behavior of the mathematical expectation of the total energy of a harmonic oscillator without friction under the influence of an energy pump with a controlling element of the form of a stochastic harmonic oscillator without friction with a white noise perturbation in resonant and non-resonant cases is found. During the analytical solving the problem of finding the mathematical expectation of the total energy of a harmonic oscillator with random perturbation, the properties of the Wiener process, the stochastic Ito integral, and the mathematical expectation of the product of stochastic integrals are used.Key words: harmonic oscillator, total energy, white noise.Pages of the article in the issue: 47 - 52Language of the article: Ukrainian
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