Electronic Communications in Probability

Hausdorff dimension of the record set of a fractional Brownian motion

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

Full-text: Open access

Abstract

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

Article information

Source
Electron. Commun. Probab., Volume 23 (2018), paper no. 22, 8 pp.

Dates
Received: 19 September 2017
Accepted: 27 February 2018
First available in Project Euclid: 30 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1522375381

Digital Object Identifier
doi:10.1214/18-ECP121

Mathematical Reviews number (MathSciNet)
MR3785396

Zentralblatt MATH identifier
1390.60143

Subjects
Primary: 60G22: Fractional processes, including fractional Brownian motion 60G17: Sample path properties 60G18: Self-similar processes 28A78: Hausdorff and packing measures 28A80: Fractals [See also 37Fxx]

Keywords
fractional Brownian motion record set Hausdorff dimension

Rights
Creative Commons Attribution 4.0 International License.

Citation

Benigni, Lucas; Cosco, Clément; Shapira, Assaf; Wiese, Kay Jörg. Hausdorff dimension of the record set of a fractional Brownian motion. Electron. Commun. Probab. 23 (2018), paper no. 22, 8 pp. doi:10.1214/18-ECP121. https://projecteuclid.org/euclid.ecp/1522375381


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