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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 Pregaussian class ： ウィキペディア英語版 Pregaussian class In probability theory, a pregaussian class or pregaussian set of functions is a set of functions, square integrable with respect to some probability measure, such that there exists a certain Gaussian process, indexed by this set, satisfying the conditions below. ==Definition== For a probability space (''S'', Σ, ''P''), denote by $L^2\_P(S)$ a set of square integrable with respect to ''P'' functions $f:S\backslash to\; R$, that is : Consider a set $\backslash mathcal\backslash subset\; L^2\_P(S)$. There exists a Gaussian process $G\_P$, indexed by $\backslash mathcal$, with mean 0 and covariance :$\backslash operatorname\; (G\_P(f),G\_P(g))=\; E\; G\_P(f)G\_P(g)=\backslash int\; fg\backslash ,\; dP-\backslash int\; f\backslash ,dP\; \backslash int\; g\backslash ,dP\backslash textf,g\backslash in\backslash mathcal$ Such a process exists because the given covariance is positive definite. This covariance defines a semi-inner product as well as a pseudometric on $L^2\_P(S)$ given by :$\backslash varrho\_P(f,g)=(E(G\_P(f)-G\_P(g))^2)^$ Definition A class $\backslash mathcal\backslash subset\; L^2\_P(S)$ is called pregaussian if for each $\backslash omega\backslash in\; S,$ the function $f\backslash mapsto\; G\_P(f)(\backslash omega)$ on $\backslash mathcal$ is bounded, $\backslash varrho\_P$-uniformly continuous, and prelinear. 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「Pregaussian class」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.