Averaging of randomly perturbed evolutionary equations
Evolutionary equations with coefficients perturbed by diffusion processes are considered. It is proved that the solutions of these equations converge weakly in distribution, as a small parameter tends to zero, to a unique solution of a martingale problem that corresponds to an evolutionary stochasti...
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| Date: | 1993 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1993
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5889 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512110231945216 |
|---|---|
| author | Kolomiets, Yu. V. Коломиец, Ю. В. Коломиец, Ю. В. |
| author_facet | Kolomiets, Yu. V. Коломиец, Ю. В. Коломиец, Ю. В. |
| author_sort | Kolomiets, Yu. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:20:04Z |
| description | Evolutionary equations with coefficients perturbed by diffusion processes are considered. It is proved that the solutions of these equations converge weakly in distribution, as a small parameter tends to zero, to a unique solution of a martingale problem that corresponds to an evolutionary stochastic equation in the case where the powers of a small parameter are inconsistent. |
| first_indexed | 2026-03-24T03:23:34Z |
| format | Article |
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| id | umjimathkievua-article-5889 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:23:34Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/d1/bdace306149bb919a9e3957254d165d1.pdf |
| spelling | umjimathkievua-article-58892020-03-19T09:20:04Z Averaging of randomly perturbed evolutionary equations Усреднение случайно возмущенных эволюционных уравнений Kolomiets, Yu. V. Коломиец, Ю. В. Коломиец, Ю. В. Evolutionary equations with coefficients perturbed by diffusion processes are considered. It is proved that the solutions of these equations converge weakly in distribution, as a small parameter tends to zero, to a unique solution of a martingale problem that corresponds to an evolutionary stochastic equation in the case where the powers of a small parameter are inconsistent. Розглядаються еволюційні рівняння з коефіцієнтами, збуреними дифузійними процесами. Доводиться слабка збіжність у розумінні розподілів розв’язків даних рівнянь при прямуванні малого параметра до нуля, до єдиного розв’язку мартингальної проблеми, що відповідає еволюційному стохастичному рівнянню, у випадку неузгодженості степенів малого параметра. Institute of Mathematics, NAS of Ukraine 1993-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5889 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 7 (1993); 963–971 Український математичний журнал; Том 45 № 7 (1993); 963–971 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5889/8461 https://umj.imath.kiev.ua/index.php/umj/article/view/5889/8462 Copyright (c) 1993 Kolomiets Yu. V. |
| spellingShingle | Kolomiets, Yu. V. Коломиец, Ю. В. Коломиец, Ю. В. Averaging of randomly perturbed evolutionary equations |
| title | Averaging of randomly perturbed evolutionary equations |
| title_alt | Усреднение случайно возмущенных эволюционных уравнений |
| title_full | Averaging of randomly perturbed evolutionary equations |
| title_fullStr | Averaging of randomly perturbed evolutionary equations |
| title_full_unstemmed | Averaging of randomly perturbed evolutionary equations |
| title_short | Averaging of randomly perturbed evolutionary equations |
| title_sort | averaging of randomly perturbed evolutionary equations |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5889 |
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