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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 Telescoping Markov chain ： ウィキペディア英語版 Telescoping Markov chain In probability theory, a telescoping Markov chain (TMC) is a vector-valued stochastic process that satisfies a Markov property and admits a hierarchical format through a network of transition matrices with cascading dependence. For any $N>\; 1$ consider the set of spaces $\backslash \_^N$. The hierarchical process $\backslash theta\_k$ defined in the product-space : $\backslash theta\_k\; =\; (\backslash theta\_k^1,.....,\backslash theta\_k^N)\backslash in\backslash mathcal\; S^1\backslash times......\backslash times\backslash mathcal\; S^N$ is said to be a TMC if there is a set of transition probability kernels $\backslash \_^N$ such that (1) $\backslash theta\_k^1$ is a Markov chain with transition probability matrix $\backslash Lambda^1$ : $\backslash mathbb\; P(\backslash theta\_k^1=s|\backslash theta\_^1=r)=\backslash Lambda^1(s|r)$ (2) there is a cascading dependence in every level of the hierarchy, : $\backslash mathbb\; P(\backslash theta\_k^n=s|\backslash theta\_^n=r,\backslash theta\_k^=t)=\backslash Lambda^n(s|r,t)$     for all $n\backslash geq\; 2.$ (3) $\backslash theta\_k$ satisfies a Markov property with a transition kernel that can be written in terms of the $\backslash Lambda$'s, :$\backslash mathbb\; P(\backslash theta\_=\backslash vec\; s|\backslash theta\_k=\backslash vec\; r)=\backslash Lambda^1(s\_1|r\_1)\backslash prod\_^N\backslash Lambda^\backslash ell(s\_\backslash ell|r\_\backslash ell,s\_)$ where $\backslash vec\; s\; =\; (s\_1,\backslash ldots,s\_N)\backslash in\backslash mathcal\; S^1\backslash times\backslash cdots\backslash times\backslash mathcal\; S^N$ and $\backslash vec\; r\; =\; (r\_1,\backslash ldots,r\_N)\backslash in\backslash mathcal\; S^1\backslash times\backslash cdots\backslash times\backslash mathcal\; S^N.$ 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「Telescoping Markov chain」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.