The Annals of Probability

Stationary processes whose filtrations are standard

X. Bressaud, A. Maass, S. Martinez, and J. San Martin

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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.

Article information

Source
Ann. Probab., Volume 34, Number 4 (2006), 1589-1600.

Dates
First available in Project Euclid: 19 September 2006

Permanent link to this document
https://projecteuclid.org/euclid.aop/1158673328

Digital Object Identifier
doi:10.1214/009117906000000151

Mathematical Reviews number (MathSciNet)
MR2257656

Zentralblatt MATH identifier
1104.60005

Subjects
Primary: 60A10: Probabilistic measure theory {For ergodic theory, see 28Dxx and 60Fxx} 60G10: Stationary processes

Keywords
Standard filtrations summable memory decay couplings

Citation

Bressaud, X.; Maass, A.; Martinez, S.; San Martin, J. Stationary processes whose filtrations are standard. Ann. Probab. 34 (2006), no. 4, 1589--1600. doi:10.1214/009117906000000151. https://projecteuclid.org/euclid.aop/1158673328


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