About asymptotic behavior of the mathematical expectation of the total energy of the harmonic oscillator with random perturbation - Zimin, O. I.; Kulinich, G. L. (Київський національний університет імені Тараса Шевченка, 2018)
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