Electronic Communications in Probability

Simultaneous boundary hitting by coupled reflected Brownian motions

Krzysztof Burdzy

Full-text: Open access

Abstract

Mirror coupled reflected Brownian motions can simultaneously hit opposite sides of a wedge at different distances from the origin.

Article information

Source
Electron. Commun. Probab., Volume 24 (2019), paper no. 22, 12 pp.

Dates
Received: 20 December 2018
Accepted: 1 April 2019
First available in Project Euclid: 12 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1555034600

Digital Object Identifier
doi:10.1214/19-ECP224

Mathematical Reviews number (MathSciNet)
MR3940197

Zentralblatt MATH identifier
07055626

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

Keywords
reflected Brownian motion coupling

Rights
Creative Commons Attribution 4.0 International License.

Citation

Burdzy, Krzysztof. Simultaneous boundary hitting by coupled reflected Brownian motions. Electron. Commun. Probab. 24 (2019), paper no. 22, 12 pp. doi:10.1214/19-ECP224. https://projecteuclid.org/euclid.ecp/1555034600


Export citation

References

  • [1] Rami Atar and Krzysztof Burdzy, On nodal lines of Neumann eigenfunctions, Electron. Comm. Probab. 7 (2002), 129–139.
  • [2] Rami Atar and Krzysztof Burdzy, On Neumann eigenfunctions in lip domains, J. Amer. Math. Soc. 17 (2004), no. 2, 243–265.
  • [3] Rami Atar and Krzysztof Burdzy, Mirror couplings and Neumann eigenfunctions, Indiana Univ. Math. J. 57 (2008), no. 3, 1317–1351.
  • [4] Rodrigo Bañuelos and Krzysztof Burdzy, On the “hot spots” conjecture of J. Rauch, J. Funct. Anal. 164 (1999), no. 1, 1–33.
  • [5] Richard F. Bass and Krzysztof Burdzy, Fiber Brownian motion and the “hot spots” problem, Duke Math. J. 105 (2000), no. 1, 25–58.
  • [6] Krzysztof Burdzy, The hot spots problem in planar domains with one hole, Duke Math. J. 129 (2005), no. 3, 481–502.
  • [7] Krzysztof Burdzy and Wilfrid S. Kendall, Efficient Markovian couplings: examples and counterexamples, Ann. Appl. Probab. 10 (2000), no. 2, 362–409.
  • [8] M. Cranston and Y. Le Jan, Simultaneous boundary hitting for a two point reflecting Brownian motion, Séminaire de Probabilités, XXIII, Lecture Notes in Math., vol. 1372, Springer, Berlin, 1989, pp. 234–238.
  • [9] Kiyosi Itô and Henry P. McKean, Jr., Diffusion processes and their sample paths, Springer-Verlag, Berlin-New York, 1974, Second printing, corrected, Die Grundlehren der mathematischen Wissenschaften, Band 125.
  • [10] P.-L. Lions and A.-S. Sznitman, Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math. 37 (1984), no. 4, 511–537.
  • [11] Mihai N. Pascu, Scaling coupling of reflecting Brownian motions and the hot spots problem, Trans. Amer. Math. Soc. 354 (2002), no. 11, 4681–4702.
  • [12] A. Yu. Pilipenko, Stochastic flows with reflection, Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki (2005), no. 10, 23–28, arXiv:0810.4644.