Communications in Mathematical Physics

, Volume 236, Issue 3, pp 449–475 | Cite as

Log-Infinitely Divisible Multifractal Processes

  • E. Bacry
  • J.F. Muzy


 We define a large class of multifractal random measures and processes with arbitrary log-infinitely divisible exact or asymptotic scaling law. These processes generalize within a unified framework both the recently defined log-normal Multifractal Random Walk processes (MRW) [33, 3] and the log-Poisson ``product of cylindrical pulses'' [7]. Their construction involves some ``continuous stochastic multiplication'' [36] from coarse to fine scales. They are obtained as limit processes when the finest scale goes to zero. We prove the existence of these limits and we study their main statistical properties including non-degeneracy, convergence of the moments and multifractal scaling.


Large Class Fine Scale Limit Process Random Measure Unify Framework 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • E. Bacry
    • 1
  • J.F. Muzy
    • 2
  1. 1.Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau Cedex, France. E-mail: emmanuel.bacry@polytechnique.frFR
  2. 2.CNRS, UMR 6134, Université de Corse, Grossetti, 20250 Corte, France. E-mail: muzy@univ-corse.frFR

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