An elementary proof that random Fibonacci sequences grow exponentially
نویسندگان
چکیده
منابع مشابه
How do random Fibonacci sequences grow?
We study the random Fibonacci sequences defined by F1 = F2 = F̃1 = F̃2 = 1 and for n ≥ 1, Fn+2 = Fn+1 ± Fn (linear case) and F̃n+2 = |F̃n+1 ± F̃n| (non-linear case), where each ± sign is independent and either + with probability p or − with probability 1 − p (0 < p ≤ 1). Our main result is that the exponential growth of Fn for 0 < p ≤ 1, and of F̃n for 1/3 ≤ p ≤ 1 is almost surely given by ∫ ∞ 0 log ...
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We study the random Fibonacci sequences defined by F 1 = F 2 = e F 1 = e F 2 = 1 and for n ≥ 1, F n+2 = F n+1 ± Fn (linear case) and e F n+2 = | e F n+1 ± e Fn| (non-linear case), where each ± sign is independent and either + with probability p or − with probability 1 − p (0 < p ≤ 1). Our main result is that the exponential growth of Fn for 0 < p ≤ 1, and of e Fn for 1/3 ≤ p ≤ 1 is almost surel...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2006
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2006.01.002