On random measures on spaces of trajectories and strong and weak solutions of stochastic equations
We investigate stationary random measures on spaces of sequences or functions. A new definition of a strong solution of a stochastic equation is proposed. We prove that the existence of a weak solution in the ordinary sense is equivalent to the existence of a strong measure-valued solution.
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| Дата: | 2004 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2004
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/3782 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860509916013264896 |
|---|---|
| author | Dorogovtsev, A. A. Дороговцев, А. А. Дороговцев, А. А. |
| author_facet | Dorogovtsev, A. A. Дороговцев, А. А. Дороговцев, А. А. |
| author_sort | Dorogovtsev, A. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:08:43Z |
| description | We investigate stationary random measures on spaces of sequences or functions. A new definition of a strong solution of a stochastic equation is proposed. We prove that the existence of a weak solution in the ordinary sense is equivalent to the existence of a strong measure-valued solution. |
| first_indexed | 2026-03-24T02:48:42Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-3782 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:48:42Z |
| publishDate | 2004 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/dc/f122d2be88647d22af909089a40d83dc.pdf |
| spelling | umjimathkievua-article-37822020-03-18T20:08:43Z On random measures on spaces of trajectories and strong and weak solutions of stochastic equations О случайных мерах па пространстве траекторий и сильных и слабых решениях стохастических уравнений Dorogovtsev, A. A. Дороговцев, А. А. Дороговцев, А. А. We investigate stationary random measures on spaces of sequences or functions. A new definition of a strong solution of a stochastic equation is proposed. We prove that the existence of a weak solution in the ordinary sense is equivalent to the existence of a strong measure-valued solution. Досліджуються стаціонарні випадкові міри на просторах послідовностей або функцій. Запропоновано нове означення сильного розв'язку стохастичпого рівняння. Доведено, що існування слабкого розв'язку у звичайному сенсі є еквівалентним існуванню сильного мірозначиого розв'язку. Institute of Mathematics, NAS of Ukraine 2004-05-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3782 Ukrains’kyi Matematychnyi Zhurnal; Vol. 56 No. 5 (2004); 625–633 Український математичний журнал; Том 56 № 5 (2004); 625–633 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/3782/4285 https://umj.imath.kiev.ua/index.php/umj/article/view/3782/4286 Copyright (c) 2004 Dorogovtsev A. A. |
| spellingShingle | Dorogovtsev, A. A. Дороговцев, А. А. Дороговцев, А. А. On random measures on spaces of trajectories and strong and weak solutions of stochastic equations |
| title | On random measures on spaces of trajectories and strong and weak solutions of stochastic equations |
| title_alt | О случайных мерах па пространстве траекторий и сильных и слабых решениях стохастических уравнений |
| title_full | On random measures on spaces of trajectories and strong and weak solutions of stochastic equations |
| title_fullStr | On random measures on spaces of trajectories and strong and weak solutions of stochastic equations |
| title_full_unstemmed | On random measures on spaces of trajectories and strong and weak solutions of stochastic equations |
| title_short | On random measures on spaces of trajectories and strong and weak solutions of stochastic equations |
| title_sort | on random measures on spaces of trajectories and strong and weak solutions of stochastic equations |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3782 |
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