Correlation cascades of Lévy-driven random processes

Iddo Eliazar*, Joseph Klafter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We explore the correlation-structure of a large class of random processes, driven by non-Gaussian Lévy noise sources with possibly infinite variances. Examples of such processes include Lévy motions, Lévy-driven Ornstein-Uhlenbeck motions, Lévy-driven moving-average processes, fractional Lévy motions, and fractional Lévy noises. Based on the fact that non-Gaussian Lévy noises are continuum superpositions of Poisson noises, we unveil an underlying Cascade of 'Lévy correlation functions' which characterize the process-distribution and the correlation-structure of the processes under consideration. In the case where the driving Lévy noise sources are 'fractal', the resulting cascade admits a unique scale-free form.

Original languageEnglish
Pages (from-to)1-26
Number of pages26
JournalPhysica A: Statistical Mechanics and its Applications
Volume376
Issue number1-2
DOIs
StatePublished - 15 Mar 2007

Keywords

  • Fractality
  • Long-range dependence
  • Lévy Correlation Cascades
  • Non-Gaussian Lévy noises
  • Self-similarity
  • Stable Lévy noises

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