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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| Дата: | 1997 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1997
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/5017 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | 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. |
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