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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 Kolmogorov continuity theorem ： ウィキペディア英語版 Kolmogorov continuity theorem In mathematics, the Kolmogorov continuity theorem is a theorem that guarantees that a stochastic process that satisfies certain constraints on the moments of its increments will be continuous (or, more precisely, have a "continuous version"). It is credited to the Soviet mathematician Andrey Nikolaevich Kolmogorov. ==Statement of the theorem== Let $X\; :\; [0,\; +\; \backslash infty)\; \backslash times\; \backslash Omega\; \backslash to\; \backslash mathbb^$ be a stochastic process, and suppose that for all times $T\; >\; 0$, there exist positive constants $\backslash alpha,\; \backslash beta,\; K$ such that :$\backslash mathbb\; \backslash left[\; |\; X\_\; -\; X\_\; |^\; \backslash right]\; \backslash leq\; K\; |\; t\; -\; s\; |^$ for all $0\; \backslash leq\; s,\; t\; \backslash leq\; T$. Then there exists a modification of $X$ that is a continuous process, i.e. a process $\backslash tilde\; :\; [0,\; +\; \backslash infty)\; \backslash times\; \backslash Omega\; \backslash to\; \backslash mathbb^$ such that * $\backslash tilde$ is sample continuous; * for every time $t\; \backslash geq\; 0$, $\backslash mathbb\; (X\_\; =\; \backslash tilde\_)\; =\; 1.$ Furthermore, the paths of $\backslash tilde$ are almost surely $\backslash gamma$-Hölder continuous for every . 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「Kolmogorov continuity 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.