翻訳と辞書 Words near each other ・ Komlan Assignon ・ Komlan Mally ・ Komlavi Loglo ・ Komlenac ・ Komlenović ・ Komletinci ・ Komljenović ・ Komlosaurus carbonis ・ Komló ・ Komlódtótfalu ・ Komlói Bányász SK ・ Komlói Bányász SK (men's handball) ・ Komlósd ・ Komlóska ・ Komlóstető ・ Komlós–Major–Tusnády approximation ・ Komm doch mal rüber ・ Komm Kuscheln ・ Komm zurück ・ Komm zurück/Die Banane ・ Komm, du süße Todesstunde, BWV 161 ・ Komm, gib mir deine Hand/Sie liebt dich ・ Komm, Gott Schöpfer, Heiliger Geist ・ Komm, Heiliger Geist, Herre Gott ・ Komm, Jesu, komm, BWV 229 ・ Komm, süßer Tod ・ Komm, süßer Tod (film) ・ Komm, süßer Tod (novel) ・ Komm, süßer Tod, komm selge Ruh ・ Komma Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Komlós–Major–Tusnády approximation ： ウィキペディア英語版 Komlós–Major–Tusnády approximation In theory of probability, the Komlós–Major–Tusnády approximation (also known as the KMT approximation, the KMT embedding, or the Hungarian embedding) is an approximation of the empirical process by a Gaussian process constructed on the same probability space. It is named after Hungarian mathematicians János Komlós, Gábor Tusnády, and Péter Major. ==Theory== Let $U\_1,U\_2,\backslash ldots$ be independent uniform (0,1) random variables. Define a uniform empirical distribution function as :$F\_(t)=\backslash frac\backslash sum\_^n\; \backslash mathbf\_,\backslash quad\; t\backslash in\; ().$ Define a uniform empirical process as :$\backslash alpha\_(t)=\backslash sqrt(F\_(t)-t),\backslash quad\; t\backslash in\; ().$ The Donsker theorem (1952) shows that $\backslash alpha\_(t)$ converges in law to a Brownian bridge $B(t).$ Komlós, Major and Tusnády established a sharp bound for the speed of this weak convergence. :Theorem (KMT, 1975) On a suitable probability space for independent uniform (0,1) r.v. $U\_1,U\_2\backslash ldots$ the empirical process $\backslash$ can be approximated by a sequence of Brownian bridges $\backslash$ such that ::$P\backslash left\backslash (t)-B\_n(t)|>\backslash frac\backslash leq\; b\; e^$ :for all positive integers ''n'' and all $x>0$, where ''a'', ''b'', and ''c'' are positive constants. 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「Komlós–Major–Tusnády approximation」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.