Revisiting scaling, multifractal, and multiplicative cascades with the wavelet leader lens

Patrice Abry; Stéphane Jaffard; Bruno Lashermes

doi:10.1117/12.581234

1 November 2004 Revisiting scaling, multifractal, and multiplicative cascades with the wavelet leader lens

Patrice Abry, Stéphane Jaffard, Bruno Lashermes

Proceedings Volume 5607, Wavelet Applications in Industrial Processing II; (2004) https://doi.org/10.1117/12.581234
Event: Optics East, 2004, Philadelphia, Pennsylvania, United States

Abstract

In the recent past years, scaling, random multiplicative cascades, multifractal stochastic processes became common paradigms used to analyse a large variety of different empirical times series characterised by scale invariance phenomena or properties. Scale invariance implies that no characteristic scale can be identified in data or equivalently that all scales are equally important. It also means that all scales are in relation ones with the others, hence the connection to multiplicative cascades, which, by construction, tie together a wide range of scales. Data with scale invariance are also often characterised by a high irregularity of their sample path. This variability is usually accounted for by Multifractal analysis. Hence, in applications, the three notions, scaling, multiplicative cascade and multifractal are often used ones for the others and even confusingly mixed up. These assimilations, that turned out to be fruitful in the early stages of the study of scaling, are now often responsible for misleading analysis and erroneous conclusions. Wavelet coefficients have long been used with relevance to analyse scaling. However, very recently, it has been shown that the analysis of multifractal properties can be significantly improved both conceptually and practically by the use of quantities referred to as wavelet leaders. The goals of this article are to introduce the wavelet leader based multifractal analysis, to detail its qualities and to show how it enables an insightful visit of the relationships between scaling, multifractal and multiplicative cascades.

Citation Download Citation

Patrice Abry, Stéphane Jaffard, and Bruno Lashermes "Revisiting scaling, multifractal, and multiplicative cascades with the wavelet leader lens", Proc. SPIE 5607, Wavelet Applications in Industrial Processing II, (1 November 2004); https://doi.org/10.1117/12.581234

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available