翻訳と辞書 Words near each other ・ Martinez, California ・ Martinez, California beavers ・ Martinez, Georgia ・ Martinez, Texas ・ Martinfjella ・ Marting ・ Marting, West Virginia ・ Martingale ・ Martingale (betting system) ・ Martingale (collar) ・ Martingale (probability theory) ・ Martingale (tack) ・ Martingale central limit theorem ・ Martingale difference sequence ・ Martingale pricing ・ Martingale representation theorem ・ Martingrove Collegiate Institute ・ Martinho Campos ・ Martinho da Costa Lopes ・ Martinho da Vila ・ Martinho de Araújo ・ Martinho do Nascimento ・ Martinho Ndafa Kabi ・ Martinho Oliveira ・ MARTINI ・ Martini ・ Martini & Rossi ・ Martini (automobile company) ・ Martini (cocktail) ・ Martini (quartet) 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 Martingale representation theorem ： ウィキペディア英語版 Martingale representation theorem In probability theory, the martingale representation theorem states that a random variable that is measurable with respect to the filtration generated by a Brownian motion can be written in terms of an Itô integral with respect to this Brownian motion. The theorem only asserts the existence of the representation and does not help to find it explicitly; it is possible in many cases to determine the form of the representation using Malliavin calculus. Similar theorems also exist for martingales on filtrations induced by jump processes, for example, by Markov chains. ==Statement of the theorem== Let $B\_t$ be a Brownian motion on a standard filtered probability space $(\backslash Omega,\; \backslash mathcal,\backslash mathcal\_t,\; P\; )$ and let $\backslash mathcal\_t$ be the augmentation of the filtration generated by $B$. If ''X'' is a square integrable random variable measurable with respect to $\backslash mathcal\_\backslash infty$, then there exists a predictable process ''C'' which is adapted with respect to $\backslash mathcal\_t$, such that :$X\; =\; E(X)\; +\; \backslash int\_0^\backslash infty\; C\_s\backslash ,dB\_s.$ Consequently :$E(X|\; \backslash mathcal\_t)\; =\; E(X)\; +\; \backslash int\_0^t\; C\_s\; \backslash ,\; d\; B\_s.$ 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「Martingale 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.