Almost-sure Growth Rate of Generalized Random Fibonacci sequences

Mathematics – Probability

Scientific paper

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Scientific paper

10.1214/09-AIHP312

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

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