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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 Fractional Poisson process ： ウィキペディア英語版 Fractional Poisson process In probability theory, a fractional Poisson process is a stochastic process to model the long-memory dynamics of a stream of counts. The time interval between each pair of consecutive counts follows the non-exponential power-law distribution with parameter $\backslash nu$, which has physical dimension $()=\backslash sec\; ^$, where . In other words, fractional Poisson process is non-Markov counting stochastic process which exhibits non-exponential distribution of interarrival times. The fractional Poisson process is a continuous-time process which can be thought of as natural generalization of the well-known Poisson process. Fractional Poisson probability distribution is a new member of discrete probability distributions. The fractional Poisson process, Fractional compound Poisson process and fractional Poisson probability distribution function have been invented, developed and encouraged for applications by Nick Laskin (2003) who coined the terms ''fractional Poisson process'', ''Fractional compound Poisson process'' and ''fractional Poisson probability distribution function''.〔N. Laskin, (2003), http://dx.doi.org/10.1016/S1007-5704(03)00037-6 Fractional Poisson process, Communications in Nonlinear Science and Numerical Simulation, vol. 8 issue 3–4 September–December, 2003. pp. 201–213.〕 ==Fundamentals== The fractional Poisson probability distribution captures the long-memory effect which results in the non-exponential waiting time probability distribution function empirically observed in complex classical and quantum systems. Thus, ''fractional Poisson process'' and ''fractional Poisson probability distribution function'' can be considered as natural generalization of the famous Poisson process and the Poisson probability distribution. The idea behind the fractional Poisson process was to design counting process with non-exponential waiting time probability distribution. Mathematically the idea was realized by substitution the first-order time derivative in the Kolmogorov–Feller equation for the Poisson probability distribution function with the time derivative of fractional order.〔A.I. Saichev and G.M. Zaslavsky, (1997), http://dx.doi.org/10.1063/1.166272 Fractional kinetic equations: solutions and applications, Chaos vol. 7 (1997) pp. 753–764.〕〔O. N. Repin and A. I. Saichev, (2000), http://www.springerlink.com/content/r88713p577701148 Fractional Poisson Law, Radiophysics and Quantum Electronics, vol 43, Number 9 (2000), 738-741.〕 The main outcomes are new stochastic non-Markov process – fractional Poisson process and new probability distribution function – fractional Poisson probability distribution function. 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「Fractional Poisson 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.