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Laplace Approximations for Sums of Independent Random Vectors -- The Degenerate Case --
http://hdl.handle.net/2261/1214
http://hdl.handle.net/2261/1214e6f1b6c3-30f5-493d-a602-9bdc703996be
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
jms070202.pdf (227.7 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2008-03-04 | |||||
| タイトル | ||||||
| タイトル | Laplace Approximations for Sums of Independent Random Vectors -- The Degenerate 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 |
Liang, Song
× Liang, Song |
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| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | Let $X_i, i \in {\bf N} $, be {\it i.i.d.} $B$-valued random variables, where $B$ is a real separable Banach space. Let $ Φ: B \to {\bf R} $ be a mapping. The problem is to give an asymptotic evaluation of $ Z_n = E \left( \exp \left( n Φ (\sum_{i=1}^n X_i / n ) \right) \right) $, up to a factor $ (1 + o(1)) $. Bolthausen \cite{Bolthausen} studied this problem in the case that there is a unique point maximizing $ Φ - h $, where $h$ is the so-called entropy function, and the curvature at the maximum is nonvanishing, (these two will be called as {\it nondegenerate assumptions}), with some central limit theorem assumption. Kusuoka-Liang \cite{K-L} studied the same problem, and succeeded in eliminating the central limit theorem assumption, but the nondegenerate assumptions are still left. In this paper, we study the same problem not assuming the central limit theorem assumption and the nondegenerate assumptions. | |||||
| 書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 7, 号 2, p. 195-220, 発行日 2000 |
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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 | ||||||
| MR1768464 | ||||||
| Mathmatical Subject Classification | ||||||
| 60F10(MSC1991) | ||||||
| Mathmatical Subject Classification | ||||||
| 60J60(MSC1991) | ||||||
| 出版者 | ||||||
| 出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| 原稿受領日 | ||||||
| 1999-04-28 | ||||||
