Regularity results for Kolmogorov equations in $L^2 (H, μ)$ spaces and applications
We consider the transition semigroup $R_t =e^{tsA}$ associated to an Ornstein—Uhlenbeck process in a Hilbert space $H$. We characterize, under suitable assumptions, the domain of $A$ as a subspace $W^{2,2} (H, μ)$, where $μ$ is the invariant measure associated to $R_t$. This characterization is then...
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| Date: | 1997 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
1997
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5017 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511211315003392 |
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| author | Da, Prato G. Да, Прато Г. |
| author_facet | Da, Prato G. Да, Прато Г. |
| author_sort | Da, Prato G. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:22:53Z |
| description | We consider the transition semigroup $R_t =e^{tsA}$ associated to an Ornstein—Uhlenbeck process in a Hilbert space $H$. We characterize, under suitable assumptions, the domain of $A$ as a subspace $W^{2,2} (H, μ)$, where $μ$ is the invariant measure associated to $R_t$. This characterization is then used to treat some Kolmogorov equations with variable coefficients. |
| first_indexed | 2026-03-24T03:09:17Z |
| format | Article |
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| id | umjimathkievua-article-5017 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:09:17Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/bc/e05fb582e13ecb87811eb36ff23063bc.pdf |
| spelling | umjimathkievua-article-50172020-03-18T21:22:53Z Regularity results for Kolmogorov equations in $L^2 (H, μ)$ spaces and applications Результати про регулярність для рівняння Колмогорова в просторах $L^2 (H, μ)$ та їх застосуванн Da, Prato G. Да, Прато Г. We consider the transition semigroup $R_t =e^{tsA}$ associated to an Ornstein—Uhlenbeck process in a Hilbert space $H$. We characterize, under suitable assumptions, the domain of $A$ as a subspace $W^{2,2} (H, μ)$, where $μ$ is the invariant measure associated to $R_t$. This characterization is then used to treat some Kolmogorov equations with variable coefficients. Розглядається перехідна пінгрупа $R_t =e^{tsA}$, що пов'язана з процесом Орнштейна-Уленбека у гілібертовому просторі $H$. При належних умонах находиться характеризація області визначення $A$ як підпростору $W^{2,2} (H, μ)$, де $μ$— інваріантна міра, що асоціюється з $R_t$ характеризація никористовується для розгляду деяких рівнянь Колмогорова зі змінними коефіцієнтами. Institute of Mathematics, NAS of Ukraine 1997-03-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5017 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 3 (1997); 448–457 Український математичний журнал; Том 49 № 3 (1997); 448–457 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/5017/6733 https://umj.imath.kiev.ua/index.php/umj/article/view/5017/6734 Copyright (c) 1997 Da Prato G. |
| spellingShingle | Da, Prato G. Да, Прато Г. Regularity results for Kolmogorov equations in $L^2 (H, μ)$ spaces and applications |
| title | Regularity results for Kolmogorov equations in $L^2 (H, μ)$ spaces and applications |
| title_alt | Результати про регулярність для рівняння Колмогорова в просторах $L^2 (H, μ)$ та їх застосуванн |
| title_full | Regularity results for Kolmogorov equations in $L^2 (H, μ)$ spaces and applications |
| title_fullStr | Regularity results for Kolmogorov equations in $L^2 (H, μ)$ spaces and applications |
| title_full_unstemmed | Regularity results for Kolmogorov equations in $L^2 (H, μ)$ spaces and applications |
| title_short | Regularity results for Kolmogorov equations in $L^2 (H, μ)$ spaces and applications |
| title_sort | regularity results for kolmogorov equations in $l^2 (h, μ)$ spaces and applications |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5017 |
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