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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 Brownian excursion ： ウィキペディア英語版 Brownian excursion In probability theory a Brownian excursion process is a stochastic processes that is closely related to a Wiener process (or Brownian motion). Realisations of Brownian excursion processes are essentially just realizations of a Wiener process selected to satisfy certain conditions. In particular, a Brownian excursion process is a Wiener process conditioned to be positive and to take the value 0 at time 1. Alternatively, it is a Brownian bridge process conditioned to be positive. BEPs are important because, among other reasons, they naturally arise as the limit process of a number of conditional functional central limit theorems.〔Durrett, Iglehart: Functionals of Brownian Meander and Brownian Excursion, (1975)〕 ==Definition== A Brownian excursion process, $e$, is a Wiener process (or Brownian motion) conditioned to be positive and to take the value 0 at time 1. Alternatively, it is a Brownian bridge process conditioned to be positive. Another representation of a Brownian excursion $e$ in terms of a Brownian motion process ''W'' (due to Paul Lévy and noted by Kiyoshi Itō and Henry P. McKean, Jr.〔Itô and McKean (1974, page 75)〕) is in terms of the last time $\backslash tau\_$ that ''W'' hits zero before time 1 and the first time $\backslash tau\_$ that Brownian motion $W$ hits zero after time 1:〔 :$$ \ \ \stackrel \ \left \ )|} : \ 0 \le t \le 1 \right \} . Let $\backslash tau\_m$ be the time that a Brownian bridge process $W\_0$ achieves its minimum on (). Vervaat (1979) shows that :$$ \ \ \stackrel \ \left \ . 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「Brownian excursion」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.