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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 Gamma process ： ウィキペディア英語版 Gamma process A gamma process is a random process with independent gamma distributed increments. Often written as $\backslash Gamma(t;\backslash gamma,\backslash lambda)$, it is a pure-jump increasing Lévy process with intensity measure $\backslash nu(x)=\backslash gamma\; x^\backslash exp(-\backslash lambda\; x)$, for positive $x$. Thus jumps whose size lies in the interval $()$ occur as a Poisson process with intensity $\backslash nu(x)dx.$ The parameter $\backslash gamma$ controls the rate of jump arrivals and the scaling parameter $\backslash lambda$ inversely controls the jump size. It is assumed that the process starts from a value 0 at ''t''=0. The gamma process is sometimes also parameterised in terms of the mean ($\backslash mu$) and variance ($v$) of the increase per unit time, which is equivalent to $\backslash gamma\; =\; \backslash mu^2/v$ and $\backslash lambda\; =\; \backslash mu/v$. ==Properties== Some basic properties of the gamma process are: ;marginal distribution The marginal distribution of a gamma process at time $t$, is a gamma distribution with mean $\backslash gamma\; t/\backslash lambda$ and variance $\backslash gamma\; t/\backslash lambda^2.$ ;scaling :$\backslash alpha\backslash Gamma(t;\backslash gamma,\backslash lambda)\; =\; \backslash Gamma(t;\backslash gamma,\backslash lambda/\backslash alpha)\backslash ,$ ;adding independent processes :$\backslash Gamma(t;\backslash gamma\_1,\backslash lambda)\; +\; \backslash Gamma(t;\backslash gamma\_2,\backslash lambda)\; =\; \backslash Gamma(t;\backslash gamma\_1+\backslash gamma\_2,\backslash lambda)\backslash ,$ ;moments :$\backslash mathbb(X\_t^n)\; =\; \backslash lambda^\backslash Gamma(\backslash gamma\; t+n)/\backslash Gamma(\backslash gamma\; t),\backslash \; \backslash quad\; n\backslash geq\; 0\; ,$ where $\backslash Gamma(z)$ is the Gamma function. ;moment generating function : ;correlation : The gamma process is used as the distribution for random time change in the variance gamma process. 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「Gamma process」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.