On the Csáki-Vincze transformation

نویسندگان

  • HATEM HAJRI
  • E. Csáki
  • H. HAJRI
چکیده

Csáki and Vincze have defined 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 asymptotic properties of T . We prove that T is exact: ∩ k=1 σ(T (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 continuous Lévy transform of Brownian motion.

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تاریخ انتشار 2013