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Pathwise uniqueness for reflecting Brownian motion in Euclidean domains

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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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Received: 3 February 1999 / Revised version: 2 September 1999 /¶Published online: 11 April 2000

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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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Keywords

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