Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
976913 | Physica A: Statistical Mechanics and its Applications | 2007 | 26 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Iddo Eliazar, Joseph Klafter,