Maximal brownian motions

Brossard, Jean, Émery, Michel, and Leuridan, Christophe. "Maximal brownian motions." Annales de l'I.H.P. Probabilités et statistiques 45.3 (2009): 876-886. <http://eudml.org/doc/78049>.

@article{Brossard2009,
abstract = {Let Z=(X, Y) be a planar brownian motion, $\mathcal \{Z\}$ the filtration it generates, andBa linear brownian motion in the filtration $\mathcal \{Z\}$. One says thatB(or its filtration) is maximal if no other linear $\mathcal \{Z\}$-brownian motion has a filtration strictly bigger than that ofB. For instance, it is shown in [In Séminaire de Probabilités XLI 265–278 (2008) Springer] that B is maximal if there exists a linear brownian motion C independent of B and such that the planar brownian motion (B, C) generates the same filtration $\mathcal \{Z\}$ asZ. We do not know if this sufficient condition for maximality is also necessary. We give a necessary condition for B to be maximal, and a sufficient condition which may be weaker than the existence of such a C. This sufficient condition is used to prove that the linear brownian motion ∫(X dY−Y dX)/|Z|, which governs the angular part of Z, is maximal.},
author = {Brossard, Jean, Émery, Michel, Leuridan, Christophe},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {brownian filtration; maximal brownian motion; exchange property; Brownian filtration; maximal Brownian motion},
language = {eng},
number = {3},
pages = {876-886},
publisher = {Gauthier-Villars},
title = {Maximal brownian motions},
url = {http://eudml.org/doc/78049},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Brossard, Jean
AU - Émery, Michel
AU - Leuridan, Christophe
TI - Maximal brownian motions
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2009
PB - Gauthier-Villars
VL - 45
IS - 3
SP - 876
EP - 886
AB - Let Z=(X, Y) be a planar brownian motion, $\mathcal {Z}$ the filtration it generates, andBa linear brownian motion in the filtration $\mathcal {Z}$. One says thatB(or its filtration) is maximal if no other linear $\mathcal {Z}$-brownian motion has a filtration strictly bigger than that ofB. For instance, it is shown in [In Séminaire de Probabilités XLI 265–278 (2008) Springer] that B is maximal if there exists a linear brownian motion C independent of B and such that the planar brownian motion (B, C) generates the same filtration $\mathcal {Z}$ asZ. We do not know if this sufficient condition for maximality is also necessary. We give a necessary condition for B to be maximal, and a sufficient condition which may be weaker than the existence of such a C. This sufficient condition is used to prove that the linear brownian motion ∫(X dY−Y dX)/|Z|, which governs the angular part of Z, is maximal.
LA - eng
KW - brownian filtration; maximal brownian motion; exchange property; Brownian filtration; maximal Brownian motion
UR - http://eudml.org/doc/78049
ER -