Distribution Generated by a Random Inhomogenous Fibonacci Sequence

Liptai, Kálmán and Szalay, László (2024) Distribution Generated by a Random Inhomogenous Fibonacci Sequence. MEDITERRANEAN JOURNAL OF MATHEMATICS, 21 (1). ISSN 1660-5446

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Abstract

Let G_0=0 G 0 = 0 and G_1=1 G 1 = 1 . The present study deals with the inhomogeneous version \begin{aligned} G_n=G_{n-1}+G_{n-2}+w_{n-2} \end{aligned} G n = G n - 1 + G n - 2 + w n - 2 of the Fibonacci sequence, where w_{n-2} w n - 2 takes value a with probability p , and does value b with 1-p 1 - p . We describe the probability distribution of the values of G_n G n with fixed n , and examine the properties like expected value and variance. The most challenging feature is the fractal-like structure of the distribution.

Tudományterület / tudományág

natural sciences > mathematics and computer sciences

Faculty

Not relevant

Institution

Soproni Egyetem

Item Type:	Article
SWORD Depositor:	Teszt Sword
Depositing User:	Csaba Horváth
Identification Number:	MTMT:34538292
Date Deposited:	11 Mar 2024 09:23
Last Modified:	11 Mar 2024 09:23
URI:	http://publicatio.uni-sopron.hu/id/eprint/3014

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