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.
"Stationary processes whose filtrations are standard." Ann. Probab. 34 (4) 1589 - 1600, July 2006. https://doi.org/10.1214/009117906000000151