Electronic Communications in Probability

Pathwise uniqueness for reflecting Brownian motion in certain planar Lipschitz domains

Richard Bass and Krzysztof Burdzy

Full-text: Open access

Abstract

We give a simple proof that in a Lipschitz domain in two dimensions with Lipschitz constant one, there is pathwise uniqueness for the Skorokhod equation governing reflecting Brownian motion.

Article information

Source
Electron. Commun. Probab., Volume 11 (2006), paper no. 18, 178-181.

Dates
Accepted: 30 August 2006
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465058861

Digital Object Identifier
doi:10.1214/ECP.v11-1213

Mathematical Reviews number (MathSciNet)
MR2266707

Zentralblatt MATH identifier
1110.60075

Subjects
Primary: 60J65: Brownian motion [See also 58J65]

Keywords
reflecting Brownian motion

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Bass, Richard; Burdzy, Krzysztof. Pathwise uniqueness for reflecting Brownian motion in certain planar Lipschitz domains. Electron. Commun. Probab. 11 (2006), paper no. 18, 178--181. doi:10.1214/ECP.v11-1213. https://projecteuclid.org/euclid.ecp/1465058861


Export citation

References

  • M. Barlow, K. Burdzy, H. Kaspi and A. Mandelbaum. Variably skewed Brownian motion Electr. Comm. Probab. 5 (2000), paper 6, pp. 57-66.
  • R. Bass, K. Burdzy and Z. Chen. Uniqueness for reflecting Brownian motion in lip domains Ann. I. H. Poincaré 41 (2005) 197-235.
  • R. Bass and E.P. Hsu, Pathwise uniqueness for reflecting Brownian motion in Euclidean domains. Probab. Th. Related Fields 117 (2000) 183-200.
  • I. Karatzas and S.E. Shreve. Brownian Motion and Stochastic Calculus, 2nd Edition, Springer Verlag, New York, 1991.
  • D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, 3rd ed. Springer, Berlin, 1999.