Identification and properties of real harmonizable fractional Lévy motions



Bernoulli

Identification and properties of real harmonizable fractional Lévy motions

Albert Benassi, Serge Cohen and Jacques Istas

Source: Bernoulli Volume 8, Number 1 (2002), 97-115.

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.

Keywords: identification; local asymptotic self-similarity; second-order fields; stable fields

Full-text: Access granted (open access)

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.bj/1078951091
Mathematical Reviews number (MathSciNet): MR2003b:60075
Zentralblatt MATH identifier: 1005.60052


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