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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 Random Fibonacci sequence ： ウィキペディア英語版 Random Fibonacci sequence In mathematics, the random Fibonacci sequence is a stochastic analogue of the Fibonacci sequence defined by the recurrence relation ''f''''n'' = ''f''''n''−1 ± ''f''''n''−2, where the signs + or − are chosen at random with equal probability 1/2, independently for different ''n''. By a theorem of Harry Kesten and Hillel Furstenberg, random recurrent sequences of this kind grow at a certain exponential rate, but it is difficult to compute the rate explicitly. In 1999, Divakar Viswanath showed that the growth rate of the random Fibonacci sequence is equal to 1.1319882487943…, a mathematical constant that was later named Viswanath's constant.〔 〕 == Description == The random Fibonacci sequence is an integer random sequence , where ''f''1 = ''f''2 = 1 and the subsequent terms are determined from the random recurrence relation :$$ f_n = \begin f_+f_, & \text; \\ f_-f_, & \text. \end A run of the random Fibonacci sequence starts with 1,1 and the value of the each subsequent term is determined by a fair coin toss: given two consecutive elements of the sequence, the next element is either their sum or their difference with probability 1/2, independently of all the choices made previously. If in the random Fibonacci sequence the plus sign is chosen at each step, the corresponding run is the Fibonacci sequence , : $1,1,2,3,5,8,13,21,34,55,\backslash ldots.$ If the signs alternate in minus-plus-plus-minus-plus-plus-... pattern, the result is the sequence : $1,1,0,1,1,0,1,1,0,1,\backslash ldots.$ However, such patterns occur with vanishing probability in a random experiment. In a typical run, the terms will not follow a predictable pattern: : $1,\; 1,\; 2,\; 3,\; 1,\; -2,\; -3,\; -5,\; -2,\; -3,\; \backslash ldots$ \text +, +, +, -, -, +, -, -, \ldots. Similarly to the deterministic case, the random Fibonacci sequence may be profitably described via matrices: : where the signs are chosen independently for different ''n'' with equal probabilities for + or −. Thus :$\}\; =\; M\_M\_\backslash ldots\; M\_3\},$ where is a sequence of independent identically distributed random matrices taking values ''A'' or ''B'' with probability 1/2: : B=\begin 0 & 1 \\ -1 & 1 \end. 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「Random Fibonacci sequence」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.