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April 1996 Decreasing sequences of $\sigma$-fields and a measure change for Brownian motion
Lester Dubins, Jacob Feldman, Meir Smorodinsky, Boris Tsirelson
Ann. Probab. 24(2): 882-904 (April 1996). DOI: 10.1214/aop/1039639367

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.

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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

Information

Published: April 1996
First available in Project Euclid: 11 December 2002

zbMATH: 0870.60078
MathSciNet: MR1404533
Digital Object Identifier: 10.1214/aop/1039639367

Subjects:
Primary: 60J65
Secondary: 28C20, 60G07, 60H10

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 2 • April 1996
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