A limit theorem for a random walk in a stationary scenery coming from a hyperbolic dynamical system
Abstract
In this paper, we extend a result of Kesten and Spitzer (1979). Let us consider a stationary sequence (\k:=f(Tk(.)))\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 (\k)\k. We give examples of partially hyperbolic dynamical systems and of functions f such that n-3/4((S\1)+...+(S\k)) converges in distribution as n goes to infinity.
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