We show that there is a finitary isomorphism from a
finite state independent and identically distributed (i.i.d.) process to
the $T,T^{-1}$ process associated to one-dimensional random walk
with positive drift.
This contrasts with the situation for
simple symmetric random walk in any dimension, where it cannot be a finitary
factor of any i.i.d. process, including in $d\ge 5$, where it becomes
weak Bernoulli.
Publié le : 2003-10-14
Classification:
Finitary codings,
skew products,
random walks,
60G10,
28D99,
37A50,
37A35
@article{1068646374,
author = {Keane, Michael and Steif, Jeffrey E.},
title = {Finitary coding for the one-dimensional ${T,T^{-1}}$ process with drift},
journal = {Ann. Probab.},
volume = {31},
number = {1},
year = {2003},
pages = { 1979-1985},
language = {en},
url = {http://dml.mathdoc.fr/item/1068646374}
}
Keane, Michael; Steif, Jeffrey E. Finitary coding for the one-dimensional ${T,T^{-1}}$ process with drift. Ann. Probab., Tome 31 (2003) no. 1, pp. 1979-1985. http://gdmltest.u-ga.fr/item/1068646374/