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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 Skorokhod's representation theorem ： ウィキペディア英語版 Skorokhod's representation theorem In mathematics and statistics, Skorokhod's representation theorem is a result that shows that a weakly convergent sequence of probability measures whose limit measure is sufficiently well-behaved can be represented as the distribution/law of a pointwise convergent sequence of random variables defined on a common probability space. It is named for the Ukrainian mathematician A.V. Skorokhod. ==Statement of the theorem== Let $\backslash mu\_n$, $n\; \backslash in\; \backslash mathbb$ be a sequence of probability measures on a metric space $S$ such that $\backslash mu\_n$ converges weakly to some probability measure $\backslash mu\_\backslash infty$ on $S$ as $n\; \backslash to\; \backslash infty$. Suppose also that the support of $\backslash mu\_\backslash infty$ is separable. Then there exist random variables $X\_n$ defined on a common probability space $(\backslash Omega,\backslash mathcal,\backslash mathbf)$ such that the law of $X\_n$ is $\backslash mu\_n$ for all $n$ (including $n=\backslash infty$) and such that $X\_n$ converges to $X\_\backslash infty$, $\backslash mathbf$-almost surely. 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「Skorokhod's representation 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.