Correlation cascades of Lévy-driven random processes

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• 作者：Iddo Eliazar ; Joseph Klafter
• 关键词：Non-Gaussian L&#xe9 ; vy noises ; Stable L&#xe9 ; vy noises ; Self-similarity ; Fractality ; L&#xe9 ; vy Correlation Cascades ; Long-range dependence
• 刊名：Physica A
• 出版年：2007
• 期刊代码：138_03784371
• 类别：et
• 出版时间：15 March 2007
• 卷：376
• 期：Complete
• 页码：1-26
• 文件大小：352 K

摘要

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.