Identification and properties of real harmonizable fractional Lévy motions
type: Item
instance of: scholarly article
title: Identification and properties of real harmonizable fractional Lévy motions
zbMATH Open document ID: 1005.60052
author: Albert Benassi
author: Serge Cohen
author: Jacques Istas
published in: Bernoulli
publication date: 2003-02-13T00:00:00Z
review text: The authors construct a real harmonizable fractional Lévy motion (RHFLM) as a real-valued field \( X_H \) which admits the integral representation \[ X_H(x) = \int_{R^d}\frac{e^{ix\xi}-1}{\|\xi\|^{d/2 + H}}L(d\xi). \] Here \( L(d\xi) \) is the sum of a Wiener measure \( W(d\xi) \) and of an independent Lévy measure \( M(d\xi) \) the control measure of which (a) has moments of order \(p\), \(\forall p \geq 2\); (b) is rotationally invariant. The authors show that these fields are locally self-similar and the corresponding tangent field is an FBM. Furthermore, the sample paths of the RHFLM are a.s. Hölder-continuous with exponent \( H \). In the last section the fractional index \( H \) is estimated using a generalized quadratic variation.
Mathematics Subject Classification ID: 60G18
zbMATH DE Number: 1786695
zbMATH Keywords: fractional Lévy motion
zbMATH Keywords: local asymptotic self-similarity
zbMATH Keywords: stable fields
reviewed by: Elisaveta Pancheva
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1786695