Stationary processes whose filtrations are standard
Probability
2007-06-13 v2 Statistics Theory
Statistics Theory
Abstract
We study the standard property of the natural filtration associated to a 0--1 valued stationary process. In our main result we show that if the process has summable memory decay, then the associated filtration is standard. We prove it by coupling techniques. For a process whose associated filtration is standard, we construct a product type filtration extending it, based upon the usual couplings and the Vershik's criterion for standardness.
Keywords
Cite
@article{arxiv.math/0509317,
title = {Stationary processes whose filtrations are standard},
author = {X. Bressaud and A. Maass and S. Martinez and J. San Martin},
journal= {arXiv preprint arXiv:math/0509317},
year = {2007}
}
Comments
Published at http://dx.doi.org/10.1214/009117906000000151 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)