{"created":"2021-03-01T06:59:49.501909+00:00","id":40231,"links":{},"metadata":{"_buckets":{"deposit":"64972aa3-5bf8-4dd6-acda-88e9c1279190"},"_deposit":{"id":"40231","owners":[],"pid":{"revision_id":0,"type":"depid","value":"40231"},"status":"published"},"_oai":{"id":"oai:repository.dl.itc.u-tokyo.ac.jp:00040231","sets":["312:6865:7017:7023","9:504:6868:7019:7024"]},"item_4_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2000","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"2","bibliographicPageEnd":"220","bibliographicPageStart":"195","bibliographicVolumeNumber":"7","bibliographic_titles":[{"bibliographic_title":"Journal of mathematical sciences, the University of Tokyo"}]}]},"item_4_description_13":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_4_description_5":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"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.","subitem_description_type":"Abstract"}]},"item_4_publisher_20":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"Graduate School of Mathematical Sciences, The University of Tokyo"}]},"item_4_source_id_10":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA11021653","subitem_source_identifier_type":"NCID"}]},"item_4_source_id_8":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"13405705","subitem_source_identifier_type":"ISSN"}]},"item_4_subject_15":{"attribute_name":"日本十進分類法","attribute_value_mlt":[{"subitem_subject":"415","subitem_subject_scheme":"NDC"}]},"item_4_text_16":{"attribute_name":"Mathematical Reviews Number","attribute_value_mlt":[{"subitem_text_value":"MR1768464"}]},"item_4_text_17":{"attribute_name":"Mathmatical Subject Classification","attribute_value_mlt":[{"subitem_text_value":"60F10(MSC1991)"},{"subitem_text_value":"60J60(MSC1991)"}]},"item_4_text_33":{"attribute_name":"原稿受領日","attribute_value_mlt":[{"subitem_text_value":"1999-04-28"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Liang, Song"}],"nameIdentifiers":[{"nameIdentifier":"138829","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2017-06-27"}],"displaytype":"detail","filename":"jms070202.pdf","filesize":[{"value":"227.7 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"jms070202.pdf","url":"https://repository.dl.itc.u-tokyo.ac.jp/record/40231/files/jms070202.pdf"},"version_id":"be0173ea-38f3-40d7-9a39-eed2feff45d2"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"Laplace Approximations for Sums of Independent Random Vectors -- The Degenerate Case --","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Laplace Approximations for Sums of Independent Random Vectors -- The Degenerate Case --"}]},"item_type_id":"4","owner":"1","path":["7023","7024"],"pubdate":{"attribute_name":"公開日","attribute_value":"2008-03-04"},"publish_date":"2008-03-04","publish_status":"0","recid":"40231","relation_version_is_last":true,"title":["Laplace Approximations for Sums of Independent Random Vectors -- The Degenerate Case --"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-19T04:15:29.041774+00:00"}