TY - JOUR

T1 - Decreasing sequences of σ-fields and a measure change for brownian motion

AU - Dubins, Lester

AU - Feldman, Jacob

AU - Smorodinsky, Meir

AU - Tsirelson, Boris

PY - 1996/4

Y1 - 1996/4

N2 - 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.

AB - 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.

KW - Brownian filtration

KW - Decreasing sequence of measurable partitions

KW - Equivalent measure

UR - http://www.scopus.com/inward/record.url?scp=0001077760&partnerID=8YFLogxK

U2 - 10.1214/aop/1039639367

DO - 10.1214/aop/1039639367

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AN - SCOPUS:0001077760

VL - 24

SP - 882

EP - 904

JO - Annals of Probability

JF - Annals of Probability

SN - 0091-1798

IS - 2

ER -