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Séminaire de Probabilités XXIV 1988/89 pp 194–209Cite as

On pathwise uniqueness and expansion of filtrations

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Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1426))

Abstract

Suppose that pathwise uniqueness holds for the SDE Xt=x0+3 £ to σ(Xs)dBs where |σ is bounded and bounded away from 0, and B is a Brownian motion on a filtered probability space, (Ω,F,F t,P). We give conditions under which pathwise uniqueness continues to hold in the enlarged filtration (F Lt ), where L is the end of an (F t)-optional set.

Partially supported by an NSF grant through Cornell University.

Research partially supported by an NSERC of Canada operating grant.

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Author information

Authors and Affiliations

  1. Statistical Laboratory, 16 Mill Lane, CB2 1SB, Cambridge, UK

    Martin T. Barlow & Edwin A. Perkins

  2. Department of Mathematics, University of British Columbia, V6T 1Y4, Vancouver, B.C., Canada

    Martin T. Barlow & Edwin A. Perkins

Authors
  1. Martin T. Barlow
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  2. Edwin A. Perkins
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Editor information

Jacques Azéma Marc Yor Paul André Meyer

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© 1990 Springer-Verlag

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Barlow, M.T., Perkins, E.A. (1990). On pathwise uniqueness and expansion of filtrations. In: Azéma, J., Yor, M., Meyer, P.A. (eds) Séminaire de Probabilités XXIV 1988/89. Lecture Notes in Mathematics, vol 1426. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083766

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  • DOI: https://doi.org/10.1007/BFb0083766

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52694-0

  • Online ISBN: 978-3-540-47098-4

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