Power-law-distributed level crossings define fractal behavior

K. I. Hopcraft, P. C. Ingrey, and E. Jakeman
Phys. Rev. E 76, 031134 – Published 27 September 2007

Abstract

A relationship is established between the autocorrelation function of continuous Gaussian and non-Gaussian stochastic processes and the discrete process that describes their zero or level crossings. Random fractals occur when the distribution for the number of crossings is described by a class of Markov processes whose singlefold statistics are the discrete analog of the Lévy-stable continuous probability densities.

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  • Received 11 May 2007

DOI:https://doi.org/10.1103/PhysRevE.76.031134

©2007 American Physical Society

Authors & Affiliations

K. I. Hopcraft, P. C. Ingrey, and E. Jakeman

  • School of Mathematical Sciences, Applied Mathematics Division, University of Nottingham, Nottingham, NG7 2RD, United Kingdom

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Issue

Vol. 76, Iss. 3 — September 2007

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