Let $(F_t)_{t \geq 0}$ be the filtration of a Brownian motion
$(B(t))_{t \geq 0}on $(\Omega,F,P)$. An example is given of a measure $Q \sim
P$ (in the sense of absolute continuity) for which $(F_t)_{t \geq 0}$ is
not the filtration of any Brownian motion on $(\Omega,F,Q)$. This
settles a 15-year-old question.
Publié le : 1996-04-14
Classification:
Brownian filtration,
equivalent measure,
decreasing sequence of measurable partitions,
60J65,
28C20,
60G07,
60H10
@article{1039639367,
author = {Dubins, Lester and Feldman, Jacob and Smorodinsky, Meir and Tsirelson, Boris},
title = {Decreasing sequences of $\sigma$-fields and a measure change for
Brownian motion},
journal = {Ann. Probab.},
volume = {24},
number = {2},
year = {1996},
pages = { 882-904},
language = {en},
url = {http://dml.mathdoc.fr/item/1039639367}
}
Dubins, Lester; Feldman, Jacob; Smorodinsky, Meir; Tsirelson, Boris. Decreasing sequences of $\sigma$-fields and a measure change for
Brownian motion. Ann. Probab., Tome 24 (1996) no. 2, pp. 882-904. http://gdmltest.u-ga.fr/item/1039639367/