The Annals of Probability

Brownian earthworm

Krzysztof Burdzy, Zhen-Qing Chen, and Soumik Pal

Full-text: Open access

Abstract

We prove that the distance between two reflected Brownian motions, driven by the same white noise, outside a sphere in a $3$-dimensional flat torus does not converge to $0$, a.s., if the radius of the sphere is sufficiently small, relative to the size of the torus.

Article information

Source
Ann. Probab., Volume 41, Number 6 (2013), 4002-4049.

Dates
First available in Project Euclid: 20 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.aop/1384957781

Digital Object Identifier
doi:10.1214/12-AOP831

Mathematical Reviews number (MathSciNet)
MR3161468

Zentralblatt MATH identifier
1303.60074

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

Keywords
Reflected Brownian motion

Citation

Burdzy, Krzysztof; Chen, Zhen-Qing; Pal, Soumik. Brownian earthworm. Ann. Probab. 41 (2013), no. 6, 4002--4049. doi:10.1214/12-AOP831. https://projecteuclid.org/euclid.aop/1384957781


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