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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 Lévy process ： ウィキペディア英語版 Lévy process In probability theory, a Lévy process, named after the French mathematician Paul Lévy, is a stochastic process with independent, stationary increments: it represents the motion of a point whose successive displacements are random and independent, and statistically identical over different time intervals of the same length. A Lévy process may thus be viewed as the continuous-time analog of a random walk. The most well known examples of Lévy processes are Brownian motion and the Poisson process. Aside from Brownian motion with drift, all other proper Lévy processes have discontinuous paths. == Mathematical definition == A stochastic process $X=\backslash$ is said to be a Lévy process if it satisfies the following properties: # $X\_0=0\; \backslash ,$ almost surely # Independence of increments: For any # Continuity in probability: For any $\backslash epsilon>0$ and $t\backslash ge\; 0$ it holds that $\backslash lim\_P(|X\_-X\_t|>\backslash epsilon)=0$ If $X$ is a Lévy process then one may construct a version of $X$ such that $t\; \backslash mapsto\; X\_t$ is almost surely right continuous with left limits. 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「Lévy 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.