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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 Random measure ： ウィキペディア英語版 Random measure In probability theory, a random measure is a measure-valued random element.〔Kallenberg, O., ''Random Measures'', 4th edition. Academic Press, New York, London; Akademie-Verlag, Berlin (1986). ISBN 0-12-394960-2 . An authoritative but rather difficult reference. 〕〔Jan Grandell, Point processes and random measures, ''Advances in Applied Probability'' 9 (1977) 502-526. (JSTOR ) A nice and clear introduction. 〕 Let X be a complete separable metric space and $\backslash mathfrak(X)$ the σ-algebra of its Borel sets. A Borel measure μ on X is boundedly finite if μ(A) < ∞ for every bounded Borel set A. Let $M\_X$ be the space of all boundedly finite measures on $\backslash mathfrak(X)$. Let be a probability space, then a random measure maps from this probability space to the measurable space .A measure generally might be decomposed as: :$\backslash mu=\backslash mu\_d\; +\; \backslash mu\_a\; =\; \backslash mu\_d\; +\; \backslash sum\_^N\; \backslash kappa\_n\; \backslash delta\_,$ Here $\backslash mu\_d$ is a diffuse measure without atoms, while $\backslash mu\_a$ is a purely atomic measure. ==Random counting measure== A random measure of the form: :$\backslash mu=\backslash sum\_^N\; \backslash delta\_,$ where $\backslash delta$ is the Dirac measure, and $X\_n$ are random variables, is called a ''point process''〔〔 or random counting measure. This random measure describes the set of ''N'' particles, whose locations are given by the (generally vector valued) random variables $X\_n$. The diffuse component $\backslash mu\_d$ is null for a counting measure. In the formal notation of above a random counting measure is a map from a probability space to the measurable space a measurable space. Here $N\_X$ is the space of all boundedly finite integer-valued measures $N\; \backslash in\; M\_X$ (called counting measures). The definitions of expectation measure, Laplace functional, moment measures and stationarity for random measures follow those of point processes. Random measures are useful in the description and analysis of Monte Carlo methods, such as Monte Carlo numerical quadrature and particle filters.〔Crisan, D., ''Particle Filters: A Theoretical Perspective'', in ''Sequential Monte Carlo in Practice,'' Doucet, A., de Freitas, N. and Gordon, N. (Eds), Springer, 2001, ISBN 0-387-95146-6〕 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「Random measure」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.