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Stationary processes whose filtrations are standard

X. Bressaud·A. Maass·S. Martinez·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.

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X. Bressaud, A. Maass, S. Martinez, J. San Martin. 2006-09-25. Stationary processes whose filtrations are standard. https://doi.org/10.1214/009117906000000151

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