Numerical results on some generalized random Fibonacci sequences

Numerical results on some generalized random Fibonacci sequences

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Article ID: iaor20122346
Volume: 59
Issue: 1
Start Page Number: 233
End Page Number: 246
Publication Date: Jan 2010
Journal: Computers and Mathematics with Applications
Authors: ,
Keywords: Lyapunov
Abstract:

Random Fibonacci sequences are stochastic versions of the classical Fibonacci sequence f n + 1 = f n + f n 1 equ1 for n > 0 equ2, and f 0 = f 1 = 1 equ3, obtained by randomizing one or both signs on the right side of the defining equation and/or adding a ‘growth parameter.’ These sequences may be viewed as coming from a sequence of products of i.i.d. random matrices and their rate of growth measured by the associated Lyapunov exponent. Following the techniques presented by Embree and Trefethen in their numerical paper Embree and Trefethen (1999) , we study the behavior of the Lyapunov exponents as a function of the probability p equ4 of choosing + equ5 in the sign randomization.

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