A limit theorem for a random walk in a stationary scenery coming from a hyperbolic dynamical system

2006/01/30 by Francoise Pene, Pene, Francoise
Mathematics · #37D30 #37D50 #60F99 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #advanced mathematical theories #math.DS #msc:37D30 #msc:37D50 #msc:60F99

paper · pdf · doi:10.48550/arxiv.math/0601735

18 pages

arxiv created 2006/01/30 · arxiv updated 2009/12/01

Abstract

In this paper, we extend a result of Kesten and Spitzer (1979). Let us consider a stationary sequence (ξ_k:=f(T^k(.)))_k given by an invertible probability dynamical system and some centered function f. Let (S_n)_n be a simple symmetric random walk on Z independent of (ξ_k)_k. We give examples of partially hyperbolic dynamical systems and of functions f such that n^-3/4(ξ(S_1)+...+ξ(S_k)) converges in distribution as n goes to infinity.

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