HAL: hal-00273525, version 1

arXiv: 0804.2378

DOI: 10.1214/09-AIHP312

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Annales de l'IHP - Probabilités et Statistiques 46, 1 (2010) 135-158

Almost-sure Growth Rate of Generalized Random Fibonacci sequences

Elise Janvresse 1, Benoît Rittaud 2, 3, Thierry de la Rue 1

(2010)

We study the generalized random Fibonacci sequences defined by their first nonnegative terms and for $n\ge 1$, $F_{n+2} = \lambda F_{n+1} \pm F_{n}$ (linear case) and $\widetilde F_{n+2} = |\lambda \widetilde F_{n+1} \pm \widetilde F_{n}|$ (non-linear case), where each $\pm$ sign is independent and either $+$ with probability $p$ or $-$ with probability $1-p$ ($0

1:	Laboratoire de Mathématiques Raphaël Salem (LMRS)
	CNRS : UMR6085 – Université de Rouen
2:	Institut Galilée (IG)
	Université Paris XIII - Paris Nord
3:	Laboratoire de Mathématiques et Physique Théorique (LMPT)
	CNRS : UMR6083 – Université François Rabelais - Tours

Subject

:

Mathematics/Probability

Keyword(s): random Fibonacci sequence – Rosen continued fraction – upper Lyapunov exponent – Stern-Brocot intervals – Hecke group

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From: Elise Janvresse <>

Submitted on: Tuesday, 15 April 2008 15:10:28

Updated on: Friday, 5 March 2010 17:00:37