Université Paul Sabatier Toulouse

CNRS U.M.R. C5583
Laboratoire de Statistique et Probabilités

Identification and properties of Real Harmonizable Fractional Lévy Motions.

Auteur(s): Albert Benassi, Serge Cohen et Jacques Istas

Code(s) de Classification MSC:

Résumé: In this article the class of Real Harmonizable Fractional L\'evy Motions is introduced. It is shown that RHFLM share many properties with Fractional Brownian Motion. These fields are locally asymptotically self-similar with a constant index $ H,$ and have H\"olderian paths. Moreover the identification of $ H $ for RHFLM can be performed with the so-called generalized variation method. Besides the 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 to model phenomena with multiscale behavior.

Mots Clés: Identification, Local Asymptotic Self Similarity, Second order fields, Stable fields.

Date: 2000-12-19

Prépublication numéro: LSP-2000-20