Open Access
July 2006 Stationary processes whose filtrations are standard
X. Bressaud, A. Maass, S. Martinez, J. San Martin
Ann. Probab. 34(4): 1589-1600 (July 2006). DOI: 10.1214/009117906000000151

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.

Citation

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X. Bressaud. A. Maass. S. Martinez. J. San Martin. "Stationary processes whose filtrations are standard." Ann. Probab. 34 (4) 1589 - 1600, July 2006. https://doi.org/10.1214/009117906000000151

Information

Published: July 2006
First available in Project Euclid: 19 September 2006

zbMATH: 1104.60005
MathSciNet: MR2257656
Digital Object Identifier: 10.1214/009117906000000151

Subjects:
Primary: 60A10 , 60G10

Keywords: Couplings , Standard filtrations , summable memory decay

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 4 • July 2006
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