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
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
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