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

Lester Dubins, Jacob Feldman, Meir Smorodinsky, Boris Tsirelson

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)882-904
Number of pages23
JournalAnnals of Probability
Volume24
Issue number2
DOIs
StatePublished - Apr 1996

Keywords

  • Brownian filtration
  • Decreasing sequence of measurable partitions
  • Equivalent measure

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