Abstract
Let $(\mathscr{F}_t)_{t \geq 0}$ be the filtration of a Brownian motion $(B(t))_{t \geq 0}$ on $(\Omega,\mathscr{F},P)$. An example is given of a measure $Q \sim P$ (in the sense of absolute continuity) for which $(\mathscr{F}_t)_{t \geq 0}$ is not the filtration of any Brownian motion on $(\Omega,\mathscr{F},Q)$. This settles a 15-year-old question.
Citation
Lester Dubins. Jacob Feldman. Meir Smorodinsky. Boris Tsirelson. "Decreasing sequences of $\sigma$-fields and a measure change for Brownian motion." Ann. Probab. 24 (2) 882 - 904, April 1996. https://doi.org/10.1214/aop/1039639367
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