On the expected diameter of planar Brownian motion

James McRedmond; Chang Xu

doi:10.1016/j.spl.2017.07.001

On the expected diameter of planar Brownian motion

James McRedmond, Chang Xu

Mathematics And Statistics

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

5 Citations (Scopus)

33 Downloads (Pure)

Abstract

Known results show that the diameter d1 of the trace of planar Brownian motion run for unit time satisfies 1.595 ≤ Ed1 ≤ 2.507. This note improves these bounds to 1.601 ≤ Ed1 ≤ 2.355. Simulations suggest that Ed1 ≈ 1.99.

Original language	English
Pages (from-to)	1-4
Number of pages	4
Journal	Statistics and Probability Letters
Volume	130
Early online date	14 Jul 2017
DOIs	https://doi.org/10.1016/j.spl.2017.07.001
Publication status	Published - 30 Nov 2017

Keywords

Brownian motion
convex hull
diameter

Access to Document

10.1016/j.spl.2017.07.001

McRedmond-Xu-SPL-2017-On-the-expected-diameter-of-planar-BrownianAccepted author manuscript, 208 KBLicence: CC BY-NC-ND 4.0

http://dro.dur.ac.uk/22592/Licence: CC BY-NC-ND 4.0

Cite this

@article{74e6c0096c2f4b84a6bc6c09fda7ac77,

title = "On the expected diameter of planar Brownian motion",

abstract = "Known results show that the diameter d1 of the trace of planar Brownian motion run for unit time satisfies 1.595 ≤ Ed1 ≤ 2.507. This note improves these bounds to 1.601 ≤ Ed1 ≤ 2.355. Simulations suggest that Ed1 ≈ 1.99.",

keywords = "Brownian motion, convex hull, diameter",

author = "James McRedmond and Chang Xu",

year = "2017",

month = nov,

day = "30",

doi = "10.1016/j.spl.2017.07.001",

language = "English",

volume = "130",

pages = "1--4",

journal = "Statistics and Probability Letters ",

issn = "0167-7152",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - On the expected diameter of planar Brownian motion

AU - McRedmond, James

AU - Xu, Chang

PY - 2017/11/30

Y1 - 2017/11/30

N2 - Known results show that the diameter d1 of the trace of planar Brownian motion run for unit time satisfies 1.595 ≤ Ed1 ≤ 2.507. This note improves these bounds to 1.601 ≤ Ed1 ≤ 2.355. Simulations suggest that Ed1 ≈ 1.99.

AB - Known results show that the diameter d1 of the trace of planar Brownian motion run for unit time satisfies 1.595 ≤ Ed1 ≤ 2.507. This note improves these bounds to 1.601 ≤ Ed1 ≤ 2.355. Simulations suggest that Ed1 ≈ 1.99.

KW - Brownian motion

KW - convex hull

KW - diameter

UR - https://www.sciencedirect.com/journal/statistics-and-probability-letters

U2 - 10.1016/j.spl.2017.07.001

DO - 10.1016/j.spl.2017.07.001

M3 - Article

SN - 0167-7152

VL - 130

SP - 1

EP - 4

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

On the expected diameter of planar Brownian motion

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this