翻訳と辞書 Words near each other ・ Adaptations of The Phantom of the Opera ・ Adaptations of The Picture of Dorian Gray ・ Adaptations of The Wizard of Oz ・ Adaptations of Twenty Thousand Leagues Under the Sea ・ Adaptations of works by Robert E. Howard ・ Adaptations of Wuthering Heights ・ Adaptatsiya ・ Adaptatziya ・ Adaptaur ・ Adaptavist ・ Adaptec ・ Adapted automobile ・ Adapted Conventional Armed Forces in Europe Treaty ・ Adapted live stage tours ・ Adapted physical education ・ Adapted process ・ Adapter ・ Adapter (computing) ・ Adapter (disambiguation) ・ Adapter (genetics) ・ Adapter (rocketry) ・ Adapter molecule crk ・ Adapter pattern ・ Adapteva ・ Adaptin ・ Adapting Minds ・ Adaptiv ・ Adaptive algorithm ・ Adaptive architecture ・ Adaptive autonomy 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 Adapted process ： ウィキペディア英語版 Adapted process In the study of stochastic processes, an adapted process (or non-anticipating process) is one that cannot "see into the future". An informal interpretation is that ''X'' is adapted if and only if, for every realisation and every ''n'', ''Xn'' is known at time ''n''. The concept of an adapted process is essential, for instance, in the definition of the Itō integral, which only makes sense if the integrand is an adapted process. ==Definition== Let * $(\backslash Omega,\; \backslash mathcal,\; \backslash mathbb)$ be a probability space; * $I$ be an index set with a total order $\backslash leq$ (often, $I$ is $\backslash mathbb$, $\backslash mathbb\_0$, $(T)$ or $[0,\; +\backslash infty)$); * $\backslash mathcal\_\; =\; \backslash left(\backslash mathcal\_i\backslash right)\_$ be a filtration of the sigma algebra $\backslash mathcal$; * $(S,\backslash Sigma)$ be a measurable space, the ''state space''; * $X:\; I\; \backslash times\; \backslash Omega\; \backslash to\; S$ be a stochastic process. The process $X$ is said to be adapted to the filtration $\backslash left(\backslash mathcal\_i\backslash right)\_$ if the random variable $X\_i:\; \backslash Omega\; \backslash to\; S$ is a $(\backslash mathcal\_i,\; \backslash Sigma)$-measurable function for each $i\; \backslash in\; I$. 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「Adapted process」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.