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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 Stochastic kernel ： ウィキペディア英語版 Markov kernel In probability theory, a Markov kernel (or stochastic kernel) is a map that plays the role, in the general theory of Markov processes, that the transition matrix does in the theory of Markov processes with a finite state space. == Formal definition == Let $(X,\backslash mathcal\; A)$, $(Y,\backslash mathcal\; B)$ be measurable spaces. A ''Markov kernel'' with source $(X,\backslash mathcal\; A)$ and target $(Y,\backslash mathcal\; B)$ is a map $\backslash kappa\; \backslash colon\; X\; \backslash times\; \backslash mathcal\; B\; \backslash to\; ()$ with the following properties: # The map $x\; \backslash mapsto\; \backslash kappa(x,B)$ is $\backslash mathcal\; A$ - measureable for every $B\; \backslash in\; \backslash mathcal\; B$. # The map $B\; \backslash mapsto\; \backslash kappa(x,B)$ is a probability measure on $(Y,\; \backslash mathcal\; B)$ for every $x\; \backslash in\; X$. (i.e. It associates to each point $x\; \backslash in\; X$ a probability measure $\backslash kappa(x,.)$ on $(Y,\backslash mathcal\; B)$ such that, for every measurable set $B\backslash in\backslash mathcal\; B$, the map $x\backslash mapsto\; \backslash kappa(x,B)$ is measurable with respect to the $\backslash sigma$-algebra $\backslash mathcal\; A$.) 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「Markov kernel」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.