Properties and Hurst exponent estimation of the circularly-symmetric fractional Brownian motion

Jean François Coeurjolly; Emilio Porcu

doi:10.1016/j.spl.2017.04.005

Properties and Hurst exponent estimation of the circularly-symmetric fractional Brownian motion

Jean François Coeurjolly, Emilio Porcu

Mathematics

UQAM University

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

10 Scopus citations

Abstract

This paper extends the fractional Brownian motion to the complex-valued case. The model is defined as the centered, zero at zero, self-similar complex-valued stochastic process with stationary increments. We present a few properties of this new model and propose an estimation of its main index, the Hurst exponent characterizing the self-similarity property.

Original language	British English
Pages (from-to)	21-27
Number of pages	7
Journal	Statistics and Probability Letters
Volume	128
DOIs	https://doi.org/10.1016/j.spl.2017.04.005
State	Published - Sep 2017

Keywords

Complex-valued stochastic process
Hurst exponent estimation
Multivariate fractional Brownian motion

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10.1016/j.spl.2017.04.005

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title = "Properties and Hurst exponent estimation of the circularly-symmetric fractional Brownian motion",

abstract = "This paper extends the fractional Brownian motion to the complex-valued case. The model is defined as the centered, zero at zero, self-similar complex-valued stochastic process with stationary increments. We present a few properties of this new model and propose an estimation of its main index, the Hurst exponent characterizing the self-similarity property.",

keywords = "Complex-valued stochastic process, Hurst exponent estimation, Multivariate fractional Brownian motion",

author = "Coeurjolly, {Jean Fran{\c c}ois} and Emilio Porcu",

note = "Funding Information: Emilio Porcu is supported by Proyecto Fondecyt Regular Number 1130647 from Chilean Ministry of Science and Education. Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2017",

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AU - Coeurjolly, Jean François

AU - Porcu, Emilio

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N2 - This paper extends the fractional Brownian motion to the complex-valued case. The model is defined as the centered, zero at zero, self-similar complex-valued stochastic process with stationary increments. We present a few properties of this new model and propose an estimation of its main index, the Hurst exponent characterizing the self-similarity property.

AB - This paper extends the fractional Brownian motion to the complex-valued case. The model is defined as the centered, zero at zero, self-similar complex-valued stochastic process with stationary increments. We present a few properties of this new model and propose an estimation of its main index, the Hurst exponent characterizing the self-similarity property.

KW - Complex-valued stochastic process

KW - Hurst exponent estimation

KW - Multivariate fractional Brownian motion

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DO - 10.1016/j.spl.2017.04.005

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VL - 128

SP - 21

EP - 27

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

Properties and Hurst exponent estimation of the circularly-symmetric fractional Brownian motion

Abstract

Keywords

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