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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Slepian's lemma ： ウィキペディア英語版 Slepian's lemma In probability theory, Slepian's lemma (1962), named after David Slepian, is a Gaussian comparison inequality. It states that for Gaussian random variables $X\; =\; (X\_1,\backslash dots,X\_n)$ and $Y\; =\; (Y\_1,\backslash dots,Y\_n)$ in $\backslash mathbb^n$ satisfying $E()\; =\; E()\; =\; 0$, :$E()=E(),\; i=1,\backslash dots,n,\; \backslash text\; \backslash \; E()\; \backslash le\; E(Y\_j)$ for $i\; \backslash neq\; j$, the the following inequality holds for all real numbers $u\_1,...,u\_n$: :$P(\backslash le\; u\_1,\; \backslash dots,\; X\_n\; \backslash le\; u\_n)\; \backslash le\; P(\backslash le\; u\_1,\; \backslash dots,\; Y\_n\; \backslash le\; u\_n)$, While this intuitive-seeming result is true for Gaussian processes, it is not in general true for other random variables—not even those with expectation 0. As a corollary, if $(X\_t)\_$ is a centered stationary Gaussian process such that $E()\; \backslash geq\; 0$ for all t, it holds for any real number c that :$P\backslash left\; \backslash ge\; P\backslash left\; P\backslash left,\; \backslash quad\; T,S\; >\; 0$. ==History== Slepian's lemma was first proven by Slepian in 1962, and has since been used in reliability theory, extreme value theory and areas of pure probability. It has also been reproven in several different forms. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Slepian's lemma」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.