Let (ℱt)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 (ℱt)t≥0 is not the filtration of any Brownian motion on (Ω,ℱ,Q). This settles a 15-year-old question.
- Brownian filtration
- Decreasing sequence of measurable partitions
- Equivalent measure