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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 Cauchy process ： ウィキペディア英語版 Cauchy process In probability theory, a Cauchy process is a type of stochastic process. There are symmetric and asymmetric forms of the Cauchy process. The unspecified term "Cauchy process" is often used to refer to the symmetric Cauchy process. The Cauchy process has a number of properties: #It is a Lévy process #It is a stable process〔〔 #It is a pure jump process #Its moments are infinite. ==Symmetric Cauchy process== The symmetric Cauchy process can be described by a Brownian motion or Wiener process subject to a Lévy subordinator. The Lévy subordinator is a process associated with a Lévy distribution having location parameter of $0$ and a scale parameter of $t^2/2$.〔 The Lévy distribution is a special case of the inverse-gamma distribution. So, using $C$ to represent the Cauchy process and $L$ to represent the Lévy subordinator, the symmetric Cauchy process can be described as: :$$ C(t; 0, 1) \;:=\;W(L(t; 0, t^2/2)). The Lévy distribution is the probability of the first hitting time for a Brownian motion, and thus the Cauchy process is essentially the result of two independent Brownian motion processes.〔 The Lévy–Khintchine representation for the symmetric Cauchy process is a triplet with zero drift and zero diffusion, giving a Lévy–Khintchine triplet of $(0,0,\; W)$, where $W(dx)\; =\; dx\; /\; (\backslash pi\; x^2)$.〔 The marginal characteristic function of the symmetric Cauchy process has the form:〔〔 : :$f(x;\; t)\; =\; \backslash left(\backslash right).$ 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「Cauchy 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.