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NOTE ON AN ALMOST SURE INVARIANCE PRINCIPLE FOR SOME EMPIRICAL PROCESSES
http://hdl.handle.net/10131/5412
http://hdl.handle.net/10131/5412905ec98b-48cf-40d7-9736-26834683ed77
名前 / ファイル | ライセンス | アクション |
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YMJ_27_N2_1979_105-110.pdf (424.9 kB)
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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 | NOTE ON AN ALMOST SURE INVARIANCE PRINCIPLE FOR SOME EMPIRICAL PROCESSES | |||||
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 |
Yoshihara, Ken-ichi
× Yoshihara, Ken-ichi |
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著者所属 | ||||||
Department of Mathematics, Faculty of Engineering, Yokohama National University, Tokiwadai, Hodogaya, Yokohama, Japan | ||||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | Let $¥{¥xi_{i}¥}$ be a strictly stationary sequence of random variables which are distributed uniformly over the interval $[0,1]$ and satisfy the strong mixing (s.m.) condition (1.1) $¥alpha(n)=¥sup_{-¥infty k+'¥iota}|P(A¥cap B)-P(A)P(B)|A¥in X^{k},Be-¥prime^{¥infty}¥downarrow 0$ as $ n¥rightarrow¥infty$ , where $¥vee J_{*}^{b}$ is the a-algebra generated by $¥xi_{a},$ $¥cdots,$ $¥xi_{b}(¥alpha¥leqq b)$ . Recently, Berkes and Philipp (1977) proved an almost sure invariance principle for some empirical processes by which a functional law of the iterated logarithm for the functions of s.m. sequences, a two-dimensional functional law of the iterated logarithm, etc., are easily obtained. In this note, we shall prove that Theorem 1 in Berkes and Philipp [1] remains true under the less restrictive s.m. condition. | |||||
書誌情報 |
Yokohama Mathematical Journal = 横濱市立大學紀要. D部門, 数学 巻 27, 号 2, p. 105-110, 発行日 1979 |
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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 |