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.
|Number of pages||26|
|Journal||Physica A: Statistical Mechanics and its Applications|
|State||Published - 15 Mar 2007|
- Long-range dependence
- Lévy Correlation Cascades
- Non-Gaussian Lévy noises
- Stable Lévy noises