On Randomly Perturbed Linear Oscillating Mechanical Systems
We prove that the amplitudes and the phases of eigenoscillations of a linear oscillating system perturbed by either a fast Markov process or a small Wiener process can be described asymptotically as a diffusion process whose generator is calculated.
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| Date: | 2000 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2000
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4536 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510668794363904 |
|---|---|
| author | Skorokhod, A. V. Скороход, А. В. |
| author_facet | Skorokhod, A. V. Скороход, А. В. |
| author_sort | Skorokhod, A. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:30:52Z |
| description | We prove that the amplitudes and the phases of eigenoscillations of a linear oscillating system perturbed by either a fast Markov process or a small Wiener process can be described asymptotically as a diffusion process whose generator is calculated. |
| first_indexed | 2026-03-24T03:00:40Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4536 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:00:40Z |
| publishDate | 2000 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/ea/dd398e36c63ac000e09a20dd06611eea.pdf |
| spelling | umjimathkievua-article-45362020-03-18T20:30:52Z On Randomly Perturbed Linear Oscillating Mechanical Systems Про випадково збурені линійні коливні механічні системи Skorokhod, A. V. Скороход, А. В. We prove that the amplitudes and the phases of eigenoscillations of a linear oscillating system perturbed by either a fast Markov process or a small Wiener process can be described asymptotically as a diffusion process whose generator is calculated. Доведено, що амплітуди і фази власних коливань лінійної коливної системи, збуреної або „швидким" процесом Маркова, або ж малим віперовим процесом, можна асимптотично описати дифузійним процесом, генератор якого обчислюється. Institute of Mathematics, NAS of Ukraine 2000-09-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4536 Ukrains’kyi Matematychnyi Zhurnal; Vol. 52 No. 9 (2000); 1294-1303 Український математичний журнал; Том 52 № 9 (2000); 1294-1303 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4536/5776 https://umj.imath.kiev.ua/index.php/umj/article/view/4536/5777 Copyright (c) 2000 Skorokhod A. V. |
| spellingShingle | Skorokhod, A. V. Скороход, А. В. On Randomly Perturbed Linear Oscillating Mechanical Systems |
| title | On Randomly Perturbed Linear Oscillating Mechanical Systems |
| title_alt | Про випадково збурені линійні коливні механічні системи |
| title_full | On Randomly Perturbed Linear Oscillating Mechanical Systems |
| title_fullStr | On Randomly Perturbed Linear Oscillating Mechanical Systems |
| title_full_unstemmed | On Randomly Perturbed Linear Oscillating Mechanical Systems |
| title_short | On Randomly Perturbed Linear Oscillating Mechanical Systems |
| title_sort | on randomly perturbed linear oscillating mechanical systems |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4536 |
| work_keys_str_mv | AT skorokhodav onrandomlyperturbedlinearoscillatingmechanicalsystems AT skorohodav onrandomlyperturbedlinearoscillatingmechanicalsystems AT skorokhodav provipadkovozbureníliníjníkolivnímehaníčnísistemi AT skorohodav provipadkovozbureníliníjníkolivnímehaníčnísistemi |