Stochastic perturbations of iterations of a simple, non-expanding, nonperiodic, piecewise linear, interval-map
نویسنده
چکیده
Let g(x) = x/2 + 17/30 (mod 1), let ξi, i = 1, 2, ... be a sequence of independent, identically distributed random variables with uniform distribution on the interval [0, 1/15], define gi(x) = g(x)+ξi (mod 1) and. for n = 1, 2, ..., define g(x) = gn(gn−1(...(g1(x))...)). For x ∈ [0, 1) let μn,x denote the distribution of g(x). The purpose of this note is to show that there exists a unique probability measure μ, such that, for all x ∈ [0, 1), μn,x tends to μ as n→ ∞. This contradicts a claim by Lasota and Mackey from 1987 stating that the process has an asymptotic three-periodicity.
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