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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 Point process operation ： ウィキペディア英語版 Point process operation In probability and statistics, a point process operation is a type of mathematical operation performed on a random object known as a point process, which are often used as mathematical models of phenomena that can be represented as points randomly located in space. These operations can be purely random, deterministic or both, and are used to construct new point processes, which can be then also used as mathematical models. The operations may include removing or ''thinning'' points from a point process, combining or ''superimposing'' multiple point processes into one point process or transforming the underlying space of the point process into another space. One point process that gives particularly convenient results under point process operations is the Poisson point process,〔J. F. C. Kingman. ''Poisson processes'', volume 3. Oxford university press, 1992. 〕 hence it is often used as a mathematical model.〔〔D. Stoyan, W. S. Kendall, J. Mecke, and L. Ruschendorf. ''Stochastic geometry and its applications'', volume 2. Wiley Chichester, 1995.〕 Point process operations and the resulting point processes are used in the theory of point processes and related fields such as stochastic geometry and spatial statistics.〔 ==Point process notation== (詳細はmathematical space. They have a number of interpretations, which is reflected by the various types of point process notation.〔〔F. Baccelli and B. Błaszczyszyn. ''Stochastic Geometry and Wireless Networks, Volume II – Applications'', volume 4, No 1–2 of ''Foundations and Trends in Networking''. NoW Publishers, 2009. 〕 For example, if a point $\backslash textstyle\; x$ belongs to or is a member of a point process, denoted by $\backslash textstyle$, then this can be written as:〔 : $\backslash textstyle\; x\backslash in\; ,$ and represents the point process as a random set. Alternatively, the number of points of $\backslash textstyle$ located in some Borel set $\backslash textstyle\; B$ is often written as:〔〔 : $\backslash textstyle\; (B),$ which reflects a random measure interpretation for point processes. A point process needs to be defined on an underlying mathematical space. Often this space is ''d''-dimensional Euclidean space denoted here by $\backslash textstyle\; \backslash textbf^$, although point processes can be defined on more abstract mathematical spaces.〔 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「Point process operation」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.