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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 Stratonovich integral ： ウィキペディア英語版 Stratonovich integral In stochastic processes, the Stratonovich integral (developed simultaneously by Ruslan L. Stratonovich and D. L. Fisk) is a stochastic integral, the most common alternative to the Itō integral. Although the Ito integral is the usual choice in applied mathematics, the Stratonovich integral is frequently used in physics. In some circumstances, integrals in the Stratonovich definition are easier to manipulate. Unlike the Itō calculus, Stratonovich integrals are defined such that the chain rule of ordinary calculus holds. Perhaps the most common situation in which these are encountered is as the solution to Stratonovich stochastic differential equations (SDE). These are equivalent to Itō SDEs and it is possible to convert between the two whenever one definition is more convenient. ==Definition== The Stratonovich integral can be defined in a manner similar to the Riemann integral, that is as a limit of Riemann sums. Suppose that $W\; :\; (T)\; \backslash times\; \backslash Omega\; \backslash to\; \backslash mathbb$ is a Wiener process and $X\; :\; (T)\; \backslash times\; \backslash Omega\; \backslash to\; \backslash mathbb$ is a semimartingale adapted to the natural filtration of the Wiener process. Then the Stratonovich integral :$\backslash int\_0^T\; X\_\; \backslash circ\; \backslash mathrm\; W\_t$ is a random variable $:\; \backslash Omega\; \backslash to\; \backslash mathbb$ defined as the limit in mean square of〔Gardiner (2004), p. 98 and the comment on p. 101〕 :$\backslash sum\_^\; \backslash over\; 2\}\; \backslash left(\; W\_\; \backslash right)$ as the mesh of the partition of $(T)$ tends to 0 (in the style of a Riemann–Stieltjes integral). 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「Stratonovich integral」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.