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On the expected diameter of planar Brownian motion

McRedmond, James; Xu, Chang

On the expected diameter of planar Brownian motion Thumbnail


Authors

James McRedmond

Chang Xu



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.

Citation

McRedmond, J., & Xu, C. (2017). On the expected diameter of planar Brownian motion. Statistics and Probability Letters, 130, 1-4. https://doi.org/10.1016/j.spl.2017.07.001

Journal Article Type Article
Acceptance Date Jul 6, 2017
Online Publication Date Jul 14, 2017
Publication Date Jul 14, 2017
Deposit Date Aug 10, 2017
Publicly Available Date Mar 28, 2024
Journal Statistics and Probability Letters
Print ISSN 0167-7152
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 130
Pages 1-4
DOI https://doi.org/10.1016/j.spl.2017.07.001

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