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Asymptotic Self-Similarity and Short Time Asymptotics of Stochastic Flows
http://hdl.handle.net/2261/1361
http://hdl.handle.net/2261/1361ff0c0e92-3309-4a37-9352-02bffc267bcd
名前 / ファイル | ライセンス | アクション |
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jms040305.pdf (216.1 kB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2008-03-04 | |||||
タイトル | ||||||
タイトル | Asymptotic Self-Similarity and Short Time Asymptotics of Stochastic Flows | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | departmental bulletin paper | |||||
著者 |
Kunita, Hiroshi
× Kunita, Hiroshi |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | We study asymptotic properties of Levy flows, changing scales of the space and the time. Let $ξ_t(x), t\geq 0$ be a Levy flow on a Euclidean space ${\bf R}^d$ determined by a SDE driven by an operator stable Levy process. Consider the Levy flows $ξ^{(r)}_t(x)=γ^{(x)}_{1/r}(ξ_{rt}(x)), t\geq 0$, where $\{γ^{(x)}_r\}_{r>0}$ is a dilation, i.e., a one parameter group of diffeomorphisms of ${\bf R}^d$ with invariant point $x$ such that $γ^{(x)}_{1/r}(y)\to \infty$ as $r \to 0$ whenever $y\ e x$. We show that as $r \to 0$ $\{ξ^{(r)}_t(x), t\geq 0\}$ converge weakly to a stochastic flow $\{ξ^{(0)}_t(x), t \geq 0\}$, if we choose a suitable dilation. Further, the limit flow is self-similar with respect to the dilation, i.e., its law is invariant by the above changes of the space and the time. This fact enables us to prove that the short time asymptotics of the density function of the distribution of $ξ_t(x)$ coincides with that of the density function of the distribution of $ξ^{(0)}_t(x)$. |
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書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 4, 号 3, p. 595-619, 発行日 1997 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 13405705 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA11021653 | |||||
フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
日本十進分類法 | ||||||
主題 | 415 | |||||
主題Scheme | NDC | |||||
Mathematical Reviews Number | ||||||
MR1484603 | ||||||
Mathmatical Subject Classification | ||||||
60B15(MSC1991) | ||||||
Mathmatical Subject Classification | ||||||
60H10(MSC1991) | ||||||
Mathmatical Subject Classification | ||||||
60J30(MSC1991) | ||||||
出版者 | ||||||
出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
原稿受領日 | ||||||
1996-06-11 |