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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 Progressively measurable process ： ウィキペディア英語版 Progressively measurable process In mathematics, progressive measurability is a property in the theory of stochastic processes. A progressively measurable process, while defined quite technically, is important because it implies the stopped process is measurable. Being progressively measurable is a strictly stronger property than the notion of being an adapted process. Progressively measurable processes are important in the theory of Itō integrals. ==Definition== Let * $(\backslash Omega,\; \backslash mathcal,\; \backslash mathbb)$ be a probability space; * $(\backslash mathbb,\; \backslash mathcal)$ be a measurable space, the ''state space''; * $\backslash \; \backslash mid\; t\; \backslash geq\; 0\; \backslash \}$ be a filtration of the sigma algebra $\backslash mathcal$; * $X\; :\; \backslash times\; \backslash Omega\; \backslash to\; \backslash mathbb$ defined by $(s,\; \backslash omega)\; \backslash mapsto\; X\_\; (\backslash omega)$ is $\backslash mathrm((t))\; \backslash otimes\; \backslash mathcal\_$-measurable. This implies that $X$ is $\backslash mathcal\_$-adapted.〔 A subset $P\; \backslash subseteq\; [0,\; \backslash infty)\; \backslash times\; \backslash Omega$ is said to be progressively measurable if the process $X\_\; (\backslash omega)\; :=\; \backslash chi\_\; (s,\; \backslash omega)$ is progressively measurable in the sense defined above, where $\backslash chi\_$ is the indicator function of $P$. The set of all such subsets $P$ form a sigma algebra on $[0,\; \backslash infty)\; \backslash times\; \backslash Omega$, denoted by $\backslash mathrm$, and a process $X$ is progressively measurable in the sense of the previous paragraph if, and only if, it is $\backslash mathrm$-measurable. 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「Progressively measurable 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.