A non-cosy filtration indexed by Z is constructed. The idea underlying this construction is used to exhibit a smooth and strictly increasing time-change of ``the'' Brownian filtration, such that the time-changed filtration is not cosy---and consequently not Brownian.
@article{hal-00129581,
author = {Emery, Michel and Schachermayer, Walter},
title = {Brownian filtrations are not stable under equivalent time-changes.},
journal = {HAL},
volume = {1998},
number = {0},
year = {1998},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00129581}
}
Emery, Michel; Schachermayer, Walter. Brownian filtrations are not stable under equivalent time-changes.. HAL, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/hal-00129581/