翻訳と辞書 Words near each other ・ Malli (TV series) ・ Malli Amman Durgham ・ Malli Maduve ・ Malli Malli Chudali ・ Malli Malli Idi Rani Roju ・ Malli Mastan Babu ・ Malli Seti ・ Malli-dong ・ Mallia Franklin ・ Malliabad ・ Mallial ・ Mallian Campaign ・ Mallian Kalan ・ Malliary ・ Malliavin calculus ・ Malliavin derivative ・ Malliavin's absolute continuity lemma ・ Mallica Reynolds ・ Mallica Vajrathon ・ Malliciah Goodman ・ Mallie Hughes ・ Mallie's Sports Grill & Bar ・ Mallie, Kentucky ・ Mallig Plains ・ Mallig, Isabela ・ Malligasta ・ Malligwad ・ Mallik ・ Mallik gas hydrate site ・ Mallik Island 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 Malliavin derivative ： ウィキペディア英語版 Malliavin derivative In mathematics, the Malliavin derivative is a notion of derivative in the Malliavin calculus. Intuitively, it is the notion of derivative appropriate to paths in classical Wiener space, which are "usually" not differentiable in the usual sense. ==Definition== Let $H$ be the Cameron–Martin space, and $C\_$ denote classical Wiener space: :$H\; :=\; \backslash ^)\; \backslash ;|\backslash ;\; f(0)\; =\; 0\; \backslash \}\; :=\; \backslash \; \backslash \}$; :$C\_\; :=\; C\_\; ((T);\; \backslash mathbb^)\; :=\; \backslash ;$ By the Sobolev embedding theorem, $H\; \backslash subset\; C\_0$. Let :$i\; :\; H\; \backslash to\; C\_$ denote the inclusion map. Suppose that $F\; :\; C\_\; \backslash to\; \backslash mathbb$ is Fréchet differentiable. Then the Fréchet derivative is a map :$\backslash mathrm\; F\; :\; C\_\; \backslash to\; \backslash mathrm\; (C\_;\; \backslash mathbb);$ i.e., for paths $\backslash sigma\; \backslash in\; C\_$, $\backslash mathrm\; F\; (\backslash sigma)\backslash ;$ is an element of $C\_^$, the dual space to $C\_\backslash ;$. Denote by $\backslash mathrm\_\; F(\backslash sigma)\backslash ;$ the continuous linear map $H\; \backslash to\; \backslash mathbb$ defined by :$\backslash mathrm\_\; F\; (\backslash sigma)\; :=\; \backslash mathrm\; F\; (\backslash sigma)\; \backslash circ\; i\; :\; H\; \backslash to\; \backslash mathbb,$ sometimes known as the ''H''-derivative. Now define $\backslash nabla\_\; F\; :\; C\_\; \backslash to\; H$ to be the adjoint of $\backslash mathrm\_\; F\backslash ;$ in the sense that :$\backslash int\_0^T\; \backslash left(\backslash partial\_t\; \backslash nabla\_H\; F(\backslash sigma)\backslash right)\; \backslash cdot\; \backslash partial\_t\; h\; :=\; \backslash langle\; \backslash nabla\_\; F\; (\backslash sigma),\; h\; \backslash rangle\_\; =\; \backslash left(\; \backslash mathrm\_\; F\; \backslash right)\; (\backslash sigma)\; (h)\; =\; \backslash lim\_\; \backslash frac.$ Then the Malliavin derivative $\backslash mathrm\_$ is defined by :$\backslash left(\; \backslash mathrm\_\; F\; \backslash right)\; (\backslash sigma)\; :=\; \backslash frac\; \backslash left(\; \backslash left(\; \backslash nabla\_\; F\; \backslash right)\; (\backslash sigma)\; \backslash right).$ The domain of $\backslash mathrm\_$ is the set $\backslash mathbf$ of all Fréchet differentiable real-valued functions on $C\_\backslash ;$; the codomain is $L^\; ((T);\; \backslash mathbb^)$. The Skorokhod integral $\backslash delta\backslash ;$ is defined to be the adjoint of the Malliavin derivative: :$\backslash delta\; :=\; \backslash left(\; \backslash mathrm\_\; \backslash right)^\; :\; \backslash operatorname\; \backslash left(\; \backslash mathrm\_\; \backslash right)\; \backslash subseteq\; L^\; ((T);\; \backslash mathbb^)\; \backslash to\; \backslash mathbf^\; =\; \backslash mathrm\; (\backslash mathbf;\; \backslash mathbb).$ 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「Malliavin derivative」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.