# Decreasing sequences of $\sigma$-fields and a measure change for Brownian motion. II

@inproceedings{Dubins1996DecreasingSO,
title={Decreasing sequences of \$\sigma\$-fields and a measure change for Brownian motion. II},
author={Lester E. Dubins and Jacob Feldman and Meir Smorodinsky and Boris Tsirelson},
year={1996}
}
Let (F t ) t≥0 be the filtration of a Brownian motion (B(t))t≥0 on (Ω,F,P). An example is given of a measure Q ∼ P (in the sense of absolute continuity) for which (F t ) t ≥ 0 is not the filtration of any Brownian motion on (Ω,F,Q). This settles a 15-year-old question.

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