How do random Fibonacci sequences grow?

Details How do random Fibonacci sequences grow? How do random Fibonacci sequences grow?

2006-11-28

arxiv.org/abs/math/0611860v1

Probability Theory and Related Fields Volume 142, 3-4 (2008) 619-648

Mathematics

Probability

Scientific paper

10.1007/s00440-007-0117-7

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

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