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February 2002 Identification and properties of real harmonizable fractional Lévy motions
Albert Benassi, Serge Cohen, Jacques Istas
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Bernoulli 8(1): 97-115 (February 2002).

Abstract

The class of real harmonizable fractional Lévy motions (RHFLMs) is introduced. It is shown that these share many properties with fractional Brownian motion. These fields are locally asymptotically self-similar with a constant index H, and have Hölderian paths. Moreover, the identification of H for the RHFLMs can be performed with the so-called generalized variation method. Besides fractional Brownian motion, this class contains non-Gaussian fields that are asymptotically self-similar at infinity with a real harmonizable fractional stable motion of index \tilde{H} as tangent field. This last property should be useful in modelling phenomena with multiscale behaviour.

Citation

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Albert Benassi. Serge Cohen. Jacques Istas. "Identification and properties of real harmonizable fractional Lévy motions." Bernoulli 8 (1) 97 - 115, February 2002.

Information

Published: February 2002
First available in Project Euclid: 10 March 2004

zbMATH: 1005.60052
MathSciNet: MR2003B:60075

Keywords: Identification , local asymptotic self-similarity , second-order fields , stable fields

Rights: Copyright © 2002 Bernoulli Society for Mathematical Statistics and Probability

Vol.8 • No. 1 • February 2002
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