Geodesic
Espaces probabilis\'es filtr\'es: de la th\'eorie de Vershik au mouvement brownien, via les id\'ees de Tsirelson (Probability spaces with filtrations: from Vershik's theory to the Brownian motion via Tsirelson's ideas)
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part X, Tome 307 (2004), pp. 236-265

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This paper is a survey of the recent literature on the probabilistic theory of filtrations related to the notion of standard filtration (due to Vershik) and cozy filtration (due to Tsirelson), as well as applications of these notions for construction of probability spaces with filtrations that can be thought to be Brownian, but are not. 
@article{ZNSL_2004_307_a7,
     author = {M. \'Emery},
     title = {Espaces probabilis\'es filtr\'es: de la th\'eorie de {Vershik} au mouvement brownien, via les id\'ees de {Tsirelson} {(Probability} spaces with filtrations: from {Vershik's} theory to the {Brownian} motion via {Tsirelson's} ideas)},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {236--265},
     publisher = {mathdoc},
     volume = {307},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_307_a7/}
}
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M. Émery. Espaces probabilis\'es filtr\'es: de la th\'eorie de Vershik au mouvement brownien, via les id\'ees de Tsirelson (Probability spaces with filtrations: from Vershik's theory to the Brownian motion via Tsirelson's ideas). Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part X, Tome 307 (2004), pp. 236-265. http://geodesic.mathdoc.fr/item/ZNSL_2004_307_a7/