Properties of the Flows Generated by Stochastic Equations with Reflection
We consider properties of a random set $\varphi_t(\mathbb{R}_+^d)$, where $\varphi_t(x)$ is a solution of a stochastic differential equation in $\mathbb{R}_+^d$ with normal reflection on the boundary starting at the point $x$. We perform the characterization of inner and boundary points of the set...
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| Datum: | 2005 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2005
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3665 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | We consider properties of a random set $\varphi_t(\mathbb{R}_+^d)$, where $\varphi_t(x)$ is a solution of a stochastic differential equation in
$\mathbb{R}_+^d$ with normal reflection on the boundary starting at the point $x$. We perform the characterization of inner and boundary points of the set $\varphi_t(\mathbb{R}_+^d)$.
We prove that the Hausdorff dimension of the boundary $\partial \varphi_t(\mathbb{R}_+^d)$ is not greater than $d - 1$. |
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