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Warped infinitely divisible cascades: beyond power laws
 

Summary: Warped infinitely divisible cascades:
beyond power laws
Pierre Chainais1, Rudolf Riedi2, Patrice Abry3
1ISIMA-LIMOS UMR 6158 - UniversitŽe Blaise Pascal, Aubi`ere, France
2Depts. of Statistics and of ECE, Rice University, Houston Texas, USA
3CNRS UMR 5672, Laboratoire de Physique. ENS Lyon, France
Pierre.Chainais@isima.fr, riedi@rice.edu, Patrice.Abry@ens-lyon.fr
RŽesumŽe ­ Nous prŽesentons les dŽefinitions et synth`eses de processus stochastiques respectant des lois d'Žechelles voilŽees, qui
s'Žecartent de fažcon contr^olŽee d'un comportement en loi de puissance. Nous dŽefinissons des bruit, mouvement et marche alŽeatoire
issus de cascades infiniment divisibles (IDC) voilŽees. Nous Žetudions analytiquement le comportement des moments des accroisse-
ments de ces processus `a travers les Žechelles. Ces rŽesultats thŽeoriques sont illustrŽes sur l'exemple d'une cascade log-Normale
voilŽee. Les algorithmes de synth`ese et les fonctions Matlab utilisŽes sont disponibles sur nos pages web.
Abstract ­ We address the definitions and synthesis of stochastic processes which possess warped scaling laws that depart from
power law behaviors in a controlled manner. We define warped infinitely divisible cascading (IDC) noise, motion and random
walk. We provide a theoretical derivation of the scaling behavior of the moments of their increments. We provide numerical
simulations of a warped log-Normal cascade to illustrate these results. Algorithms for synthesis and Matlab functions are
available from our web pages.
1 Introduction
Scaling has been observed for many years in a large num-
ber of fields including natural phenomena: turbulence in

  

Source: Abry, Patrice - Laboratoire de Physique, Ecole Normale Supérieure de Lyon

 

Collections: Engineering