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Laplace Approximations for Diffusion Processes on Torus: Nondegenerate Case
http://hdl.handle.net/2261/1197
http://hdl.handle.net/2261/1197c8982699-f03a-4f05-bd14-6847d1a57799
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
jms080104.pdf (251.2 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 | Laplace Approximations for Diffusion Processes on Torus: Nondegenerate Case | |||||
| 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 |
Kusuoka, Shigeo
× Kusuoka, Shigeo |
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| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | Let $ {\bf T}^d = {\bf R}^d / {\bf Z}^d $, and consider the family of probability measures $ \{ P_x \}_{x \in {\bf T}^d} $ on $ C([0, \infty); {\bf T}^d) $ given by the infinitesimal generator $ L_0 \equiv \frac{1}{2} Δ + b \cdot \ abla $, where $b: {\bf T}^d \to {\bf R}^d $ is a continuous function. Let $ Φ $ be a mapping $ {\cal M} ({\bf T}^d) \to {\bf R} $. Under a nuclearity assumption on the second Frechet differential of $ Φ $, an asymptotic evaluation of $ Z_T^{x, y} \equiv E^{P_x} \left[ \exp \left( T Φ (\frac{1}{T} \int_0^T δ_{X_t} dt)\right) \Big| X_T = y \right]$, up to a factor $ (1 + o(1)) $, has been gotten in Bolthausen-Deuschel-Tamura \cite{B-D-T}. In this paper, we show that the same asymptotic evaluation holds without the nuclearity assumption. |
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| 書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 8, 号 1, p. 43-70, 発行日 2001 |
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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Scheme | NDC | |||||
| 主題 | 415 | |||||
| Mathematical Reviews Number | ||||||
| MR1818905 | ||||||
| Mathmatical Subject Classification | ||||||
| 60F10(MSC2000) | ||||||
| Mathmatical Subject Classification | ||||||
| 60J60(MSC2000) | ||||||
| 出版者 | ||||||
| 出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| 原稿受領日 | ||||||
| 2000-01-24 | ||||||
