Hausdorff dimension of the record set of a fractional Brownian motion

Lucas Benigni; Clément Cosco; Assaf Shapira; Kay Jörg Wiese

doi:10.1214/18-ECP121

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Home > Journals > Electron. Commun. Probab. > Volume 23 > Article

2018 Hausdorff dimension of the record set of a fractional Brownian motion

Lucas Benigni, Clément Cosco, Assaf Shapira, Kay Jörg Wiese

Electron. Commun. Probab. 23: 1-8 (2018). DOI: 10.1214/18-ECP121

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Abstract

We prove that the Hausdorff dimension of the record set of a fractional Brownian motion with Hurst parameter $H$ equals $H$.

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Lucas Benigni. Clément Cosco. Assaf Shapira. Kay Jörg Wiese. "Hausdorff dimension of the record set of a fractional Brownian motion." Electron. Commun. Probab. 23 1 - 8, 2018. https://doi.org/10.1214/18-ECP121

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Received: 19 September 2017; Accepted: 27 February 2018; Published: 2018

First available in Project Euclid: 30 March 2018

zbMATH: 1390.60143

MathSciNet: MR3785396

Digital Object Identifier: 10.1214/18-ECP121

Subjects:

Primary: 28A78 , 28A80 , 60G17 , 60G18 , 60G22

Keywords: fractional Brownian motion , Hausdorff dimension , record set

Rights: Creative Commons Attribution 4.0 International License.

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Vol.23 • 2018

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Lucas Benigni, Clément Cosco, Assaf Shapira, Kay Jörg Wiese "Hausdorff dimension of the record set of a fractional Brownian motion," Electronic Communications in Probability, Electron. Commun. Probab. 23(none), 1-8, (2018)

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