The Annals of Probability

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

Lester Dubins, Jacob Feldman, Meir Smorodinsky, and Boris Tsirelson

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Let $(F_t)_{t \geq 0}$ be the filtration of a Brownian motion $(B(t))_{t \geq 0}on $(\Omega,F,P)$. An example is given of a measure $Q \sim P$ (in the sense of absolute continuity) for which $(F_t)_{t \geq 0}$ is not the filtration of any Brownian motion on $(\Omega,F,Q)$. This settles a 15-year-old question.

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Ann. Probab., Volume 24, Number 2 (1996), 882-904.

First available in Project Euclid: 11 December 2002

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Zentralblatt MATH identifier

Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 60G07: General theory of processes 60H10: Stochastic ordinary differential equations [See also 34F05]

Brownian filtration equivalent measure decreasing sequence of measurable partitions


Dubins, Lester; Feldman, Jacob; Smorodinsky, Meir; Tsirelson, Boris. Decreasing sequences of $\sigma$-fields and a measure change for Brownian motion. Ann. Probab. 24 (1996), no. 2, 882--904. doi:10.1214/aop/1039639367.

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