Minkowski content of Brownian cut points

Nina Holden; Gregory F. Lawler; Xinyi Li; Xin Sun

doi:10.1214/21-AIHP1159

Minkowski content of Brownian cut points

Nina Holden, Gregory F. Lawler, Xinyi Li, Xin Sun

Mathematics

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

Abstract

Let W(t), 0 ≤ t ≤ T , be a Brownian motion in Rd , d = 2, 3. We say that x is a cut point for W if x = W(t) for some t ∈ (0,T ) such that W[0, t) and W(t,T ] are disjoint. In this work, we prove that a.s. the Minkowski content of the set of cut points for W exists and is finite and non-trivial.

Original language	English (US)
Pages (from-to)	455-488
Number of pages	34
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	58
Issue number	1
DOIs	https://doi.org/10.1214/21-AIHP1159
State	Published - Feb 2021

Keywords

Brownian motion
Cut point
Minkowski content

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/21-AIHP1159

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author = "Nina Holden and Lawler, {Gregory F.} and Xinyi Li and Xin Sun",

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AU - Lawler, Gregory F.

AU - Li, Xinyi

AU - Sun, Xin

PY - 2021/2

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AB - Let W(t), 0 ≤ t ≤ T , be a Brownian motion in Rd , d = 2, 3. We say that x is a cut point for W if x = W(t) for some t ∈ (0,T ) such that W[0, t) and W(t,T ] are disjoint. In this work, we prove that a.s. the Minkowski content of the set of cut points for W exists and is finite and non-trivial.

KW - Brownian motion

KW - Cut point

KW - Minkowski content

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JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 1

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Minkowski content of Brownian cut points

Abstract

Keywords

ASJC Scopus subject areas

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