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A CRITERION OF ALMOST SURE CONVERGENCE OF ASYMPTOTIC MARTINGALES IN A BANACH SPACE
http://hdl.handle.net/10131/5658
http://hdl.handle.net/10131/56584db1f33c-710e-45d8-b4a8-077d0121aba9
名前 / ファイル | ライセンス | アクション |
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YMJ_43_N1_1995_061-072.pdf (1.1 MB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2009-12-15 | |||||
タイトル | ||||||
タイトル | A CRITERION OF ALMOST SURE CONVERGENCE OF ASYMPTOTIC MARTINGALES IN A BANACH SPACE | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | departmental bulletin paper | |||||
著者 |
Kruk, Lukasz
× Kruk, Lukasz× Zieba, Wieslaw |
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著者所属 | ||||||
Institute of Mathematics, Maria Curie-Sklodowska University, pl. Marii Curie-Sklodowskiej 1, 20-031 Lublin, Poland | ||||||
著者所属 | ||||||
Institute of Mathematics, Maria Curie-Sklodowska University,pl. Marii Curie-Sklodowskiej 1,20-031 Lublin,Poland | ||||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | In this paper we give a necessary and sufficient condition for a $L^{1}$-bounded asymptotic martingale (amart) taking values in a Banach space to converge almost surely in norm: such an asymptotic martingale $(X_{n}, F_{n}, n¥geqq 1)$ converges a.s. iff it is strongly tight, i.e. for every $¥epsilon>0$ there exists a compact set $K_{¥epsilon}$ such that $ (¥bigcap_{n=1}^{¥infty}[X_{n}¥in K_{¥epsilon}])>1-¥epsilon$ . Moreover, we show that for realvalued martingales the well known theorem of Doob is, in some sense, the best possible-there exists a martingale $(X_{n}, n¥geqq 1)$ such that ¥sup_{n}E|X_{n}|^{a}<¥infty$ for every $a¥in(O, 1)$ and it diverges a.s. (in fact, it does not even converge in law, although it is strongly tight). | |||||
書誌情報 |
Yokohama Mathematical Journal = 横濱市立大學紀要. D部門, 数学 巻 43, 号 1, p. 61-72, 発行日 1995 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 00440523 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA0089285X | |||||
フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
著者版フラグ | ||||||
出版タイプ | VoR | |||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||
出版者 | ||||||
出版者 | Yokohama City University and Yokohama National University |