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Pathwise uniqueness for reflecting Brownian motion in Euclidean domains
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  • Published: June 2000

Pathwise uniqueness for reflecting Brownian motion in Euclidean domains

  • Richard F. Bass1 &
  • Elton P. Hsu2 

Probability Theory and Related Fields volume 117, pages 183–200 (2000)Cite this article

  • 138 Accesses

  • 14 Citations

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Abstract.

For a bounded C 1,α domain in ℝd we show that there exists a strong solution to the multidimensional Skorokhod equation and that weak uniqueness holds for this equation. These results imply that pathwise uniqueness and strong uniqueness hold for the Skorokhod equation.

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Authors and Affiliations

  1. Department of Mathematics, University of Connecticut, 196 Auditorium Road, Storrs, CT 06269-3009, USA. e-mail:bass@math.uconn.edu, , , , , , US

    Richard F. Bass

  2. Department of Mathematics, Northwestern University, Evanston, IL 60208, USA. e-mail:elton@math.nwu.edu, , , , , , US

    Elton P. Hsu

Authors
  1. Richard F. Bass
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  2. Elton P. Hsu
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Received: 3 February 1999 / Revised version: 2 September 1999 /¶Published online: 11 April 2000

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Cite this article

Bass, R., Hsu, E. Pathwise uniqueness for reflecting Brownian motion in Euclidean domains. Probab Theory Relat Fields 117, 183–200 (2000). https://doi.org/10.1007/s004400050003

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  • Issue Date: June 2000

  • DOI: https://doi.org/10.1007/s004400050003

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Keywords

  • Brownian Motion
  • Strong Solution
  • Strong Uniqueness
  • Weak Uniqueness
  • Euclidean Domain
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