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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 Chung–Fuchs theorem ： ウィキペディア英語版 Chung–Fuchs theorem In mathematics, the Chung–Fuchs theorem, named after Wolfgang Heinrich Johannes Fuchs and Chung Kai-lai, states that for a particle undergoing a random walk in m-dimensions, it is certain to come back infinitely often to any neighborhood of the origin on a one-dimensional line (m = 1) or two-dimensional plane (m = 2), but in three or more dimensional spaces it will leave to infinity. Specifically, if a position of the particle is described by the vector $X\_n$: $X\_n\; =\; Z\_1\; +\; ...\; +\; Z\_n$ where $Z\_1,\; Z\_2,\; ...\; ,\; Z\_n$ are independent m-dimensional vectors with a given multivariate distribution, then if $m=1$, and $E(Z\_i)=0$, or if $m=2$ and $E(Z\_i)=0$, the following holds: $\backslash forall\; \backslash epsilon>0$, However, for $m\; \backslash ge\; 3$, $\backslash forall\; A>0$, $\backslash Pr(\backslash exists\; n\_0\; \backslash ge\; 0,\; \backslash ,\; \backslash forall\; n\backslash ge\; n\_0,\; \backslash ,\; |X\_n|\; \backslash ge\; A)\; =\; 1$. ==References== *. * "On the distribution of values of sums of random variables" Chung, K.L. and Fuchs, W.H.J. Mem. Amer. Math. Soc. 1951 no.6, 12pp 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「Chung–Fuchs theorem」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.