Stationary processes whose filtrations are standard
Bressaud, X. ; Maass, A. ; Martinez, S. ; San Martin, J.
Ann. Probab., Tome 34 (2006) no. 1, p. 1589-1600 / Harvested from Project Euclid
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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.
Publié le : 2006-07-14
Classification:  Standard filtrations,  summable memory decay,  couplings,  60A10,  60G10 
@article{1158673328,
     author = {Bressaud, X. and Maass, A. and Martinez, S. and San Martin, J.},
     title = {Stationary processes whose filtrations are standard},
     journal = {Ann. Probab.},
     volume = {34},
     number = {1},
     year = {2006},
     pages = { 1589-1600},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1158673328}
}

Bressaud, X.; Maass, A.; Martinez, S.; San Martin, J. Stationary processes whose filtrations are standard. Ann. Probab., Tome 34 (2006) no. 1, pp.  1589-1600. http://gdmltest.u-ga.fr/item/1158673328/