Almost-sure growth rate of generalized random Fibonacci sequences
Annales de l'I.H.P. Probabilités et statistiques, Volume 46 (2010) no. 1, p. 135-158
We study the generalized random Fibonacci sequences defined by their first non-negative terms and for n≥1, Fn+2=λFn+1±Fn (linear case) and ̃Fn+2=|λ̃Fn+1±̃Fn| (non-linear case), where each ± sign is independent and either + with probability p or - with probability 1-p (0
On considère les suites de Fibonacci aléatoires généralisées, définies par leurs deux premiers termes (positifs ou nuls) et, pour n≥1, Fn+2=λFn+1±Fn (cas linéaire) et ̃Fn+2=|λ̃Fn+1±̃Fn| (cas non-linéaire). Chaque signe ± est choisi indépendemment, + avec probabilité p ou - avec probabilité 1-p (0
DOI : https://doi.org/10.1214/09-AIHP312
Classification:  37H15,  60J05,  11J70
Keywords: random Fibonacci sequence, Rosen continued fraction, upper Lyapunov exponent, Stern-Brocot intervals, Hecke group
@article{AIHPB_2010__46_1_135_0,
     author = {Janvresse, \'Elise and Rittaud, Beno\^\i t and de la Rue, Thierry},
     title = {Almost-sure growth rate of generalized random Fibonacci sequences},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {46},
     number = {1},
     year = {2010},
     pages = {135-158},
     doi = {10.1214/09-AIHP312},
     zbl = {1201.37091},
     mrnumber = {2641774},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2010__46_1_135_0}
}
Janvresse, Élise; Rittaud, Benoît; de la Rue, Thierry. Almost-sure growth rate of generalized random Fibonacci sequences. Annales de l'I.H.P. Probabilités et statistiques, Volume 46 (2010) no. 1, pp. 135-158. doi : 10.1214/09-AIHP312. http://www.numdam.org/item/AIHPB_2010__46_1_135_0/

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