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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 Tanaka's formula ： ウィキペディア英語版 Tanaka's formula In the stochastic calculus, Tanaka's formula states that :$|B\_t|\; =\; \backslash int\_0^t\; \backslash sgn(B\_s)\backslash ,\; dB\_s\; +\; L\_t$ where ''B''''t'' is the standard Brownian motion, sgn denotes the sign function : and ''L''''t'' is its local time at 0 (the local time spent by ''B'' at 0 before time ''t'') given by the ''L''2-limit :$L\_\; =\; \backslash lim\_\; \backslash frac1\; |\; \backslash \; |.$ ==Properties== Tanaka's formula is the explicit Doob–Meyer decomposition of the submartingale |''B''''t''| into the martingale part (the integral on the right-hand side), and a continuous increasing process (local time). It can also be seen as the analogue of Itō's lemma for the (nonsmooth) absolute value function $f(x)=|x|$, with $f\text{'}(x)\; =\; \backslash sgn(x)$ and $f\text{'}\text{'}(x)\; =\; 2\backslash delta(x)$; see local time for a formal explanation of the Itō term. 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「Tanaka's formula」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.