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Pathwise uniqueness for perturbed versions of Brownian motion and reflected Brownian motion
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  • Published: March 1999

Pathwise uniqueness for perturbed versions of Brownian motion and reflected Brownian motion

  • L. Chaumont1 &
  • R. A. Doney2 

Probability Theory and Related Fields volume 113, pages 519–534 (1999)Cite this article

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  • 40 Citations

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Abstract.

Any solution of the functional equation

where B is a Brownian motion, behaves like a reflected Brownian motion, except when it attains a new maximum: we call it an α-perturbed reflected Brownian motion. Similarly any solution of

behaves like a Brownian motion except when it attains a new maximum or minimum: we call it an α,β-doubly perturbed Brownian motion. We complete some recent investigations by showing that for all permissible values of the parameters α, α and β respectively, these equations have pathwise unique solutions, and these are adapted to the filtration of B.

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Authors and Affiliations

  1. Laboratoire de Probabilités, Tour 56, Université Pierre et Marie Curie, 4, Place Jussieu, F-75252 Paris Cedex 05, France, , , , , , FR

    L. Chaumont

  2. Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK e-mail: rad@fs2.ma.man.ac.uk, , , , , , GB

    R. A. Doney

Authors
  1. L. Chaumont
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  2. R. A. Doney
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Received: 7 November 1997 / Revised version: 13 July 1998

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Chaumont, L., Doney, R. Pathwise uniqueness for perturbed versions of Brownian motion and reflected Brownian motion. Probab Theory Relat Fields 113, 519–534 (1999). https://doi.org/10.1007/s004400050216

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  • Issue Date: March 1999

  • DOI: https://doi.org/10.1007/s004400050216

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  • Mathematics Subject Classification (1991): 60J30, 60J20
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