Stochastic Perturbations of Iterations of a Simple, Non-expanding, Nonperiodic, Piecewise Linear, Interval-map
2016 (English)Report (Other academic)
Let g(x) = x/2 + 17/30 (mod 1), let 𝝃i i = 1,2, … to 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 gn (x) = gn(gn-1(…(g1(x))…)). For x ϵ [0,1) let μn,x denote the distribution of gn(x). The purpose of this note is to show that there exists a unique probability measure μ, such that, for all x ϵ [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.
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2016. , 18 p.
LiTH-MAT-R, ISSN 0348-2960 ; 2016:05
convergence of distributions, random dynamical systems, stochastic perturbations of iterations, nonexpanding interval maps
IdentifiersURN: urn:nbn:se:liu:diva-128167ISRN: LiTH-MAT-R--2016/05--SEOAI: oai:DiVA.org:liu-128167DiVA: diva2:929708