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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 Local time (mathematics) ： ウィキペディア英語版 Local time (mathematics) In the mathematical theory of stochastic processes, local time is a stochastic process associated with diffusion processes such as Brownian motion, that characterizes the amount of time a particle has spent at a given level. Local time appears in various stochastic integration formulas, such as Tanaka's formula, if the integrand is not sufficiently smooth. It is also studied in statistical mechanics in the context of random fields. ==Formal definition== For a diffusion process $(b\_s)\_$, the local time of $b$ at the point $x$ is the stochastic process :$L^x(t)\; =\backslash int\_0^t\; \backslash delta(x-b(s))\backslash ,ds,$ where $\backslash delta$ is the Dirac delta function. It is a notion invented by Paul Lévy. The basic idea is that $L^x(t)$ is a (rescaled) measure of how much time $b(s)$ has spent at $x$ up to time $t$. It may be written as :$L^x(t)\; =\backslash lim\_\; \backslash frac\; \backslash int\_0^t\; 1\_$, the local time can be expressed more simply as :$L^x(t)\; =\backslash int\_0^t\; 1\_\{\backslash \{x\backslash \}\}(X\_s)\; \backslash ,\; ds.$ 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「Local time (mathematics)」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.