How do random Fibonacci sequences grow?

Elise Janvresse (1) , Benoît Rittaud (2) , Thierry de La Rue (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem
2 LAGA - Laboratoire Analyse, Géométrie et Applications

We study two kinds of random Fibonacci sequences defined by $F_1=F_2=1$ and for $n\ge 1$, $F_{n+2} = F_{n+1} \pm F_{n}$ (linear case) or $F_{n+2} = |F_{n+1} \pm F_{n}|$ (non-linear case), where each sign is independent and either + with probability $p$ or - with probability $1-p$ ($0

Mots clés: random Fibonacci sequence; continued fraction; upper Lyapunov exponent; Stern-Brocot intervals

Domaines: Probabilités [math.PR]

Elise Janvresse, Benoît Rittaud, Thierry de La Rue. How do random Fibonacci sequences grow?. Probability Theory and Related Fields, 2008, Volume 142 (3-4), pp.619-648. ⟨10.1007/s00440-007-0117-7⟩. ⟨hal-00116830⟩