Open AccessAbout asymptotic behavior of the mathematical expectation of the total energy of the harmonic oscillator with random perturbation
Author(s) -
O. Zimin,
G. L. Kulinich
Publication year - 2018
Publication title -
vìsnik. serìâ fìziko-matematičnì nauki/vìsnik kiì̈vsʹkogo nacìonalʹnogo unìversitetu ìmenì tarasa ševčenka. serìâ fìziko-matematičnì nauki
Language(s) - English
Resource type - Journals
eISSN - 2218-2055
pISSN - 1812-5409
DOI - 10.17721/1812-5409.2018/3.6
Subject(s) - harmonic oscillator , perturbation (astronomy) , white noise , mathematics , stochastic process , mathematical analysis , physics , quantum mechanics , statistics
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.