Brownian earthworm

Krzysztof Burdzy; Zhen Qing Chen; Soumik Pal

doi:10.1214/12-AOP831

Brownian earthworm

Krzysztof Burdzy^*
, Zhen Qing Chen
, Soumik Pal

^*Corresponding author for this work

University of Washington

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	4002-4049
Number of pages	48
Journal	Annals of Probability
Volume	41
Issue number	6
DOIs	https://doi.org/10.1214/12-AOP831
Publication status	Published - Nov 2013
Externally published	Yes

Keywords

Reflected brownian motion

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10.1214/12-AOP831

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title = "Brownian earthworm",

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.",

keywords = "Reflected brownian motion",

author = "Krzysztof Burdzy and Chen, \{Zhen Qing\} and Soumik Pal",

year = "2013",

month = nov,

doi = "10.1214/12-AOP831",

language = "English",

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T1 - Brownian earthworm

AU - Burdzy, Krzysztof

AU - Chen, Zhen Qing

AU - Pal, Soumik

PY - 2013/11

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N2 - 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.

AB - 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.

KW - Reflected brownian motion

UR - https://www.scopus.com/pages/publications/84888401930

U2 - 10.1214/12-AOP831

DO - 10.1214/12-AOP831

M3 - Article

AN - SCOPUS:84888401930

SN - 0091-1798

VL - 41

SP - 4002

EP - 4049

JO - Annals of Probability

JF - Annals of Probability

IS - 6

ER -

Brownian earthworm

Abstract

Keywords

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