2012/09/02 by Hatem Hajri, Hajri, Hatem
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR
paper · pdf · doi:10.48550/arxiv.1209.0189
Title changed and various other modifications
arxiv created 2012/09/17 · arxiv updated 2012/09/18
Cs aki and Vincze have de fined in 1961 a discrete transformation T which applies to simple random walks and is measure preserving. In this paper, we are interested in ergodic and assymptotic properties of T . We prove that T is exact : ∩k≥ 1 σ(Tk(S)) is trivial for each simple random walk S and give a precise description of the lost information at each step k. We then show that, in a suitable scaling limit, all iterations of T "converge" to the corresponding iterations of the continous L evy transform of Brownian motion. Some consequences are also derived from these two results.