title: Power-law-distributed level crossings define fractal behavior.
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.
authors.affiliation: School of Mathematical Sciences, Applied Mathematics Division, University of Nottingham, Nottingham, NG7 2RD, United Kingdom.
authors.forename: K I
authors.initials: KI
authors.lastname: Hopcraft
authors.forename: P C
authors.initials: PC
authors.lastname: Ingrey
authors.forename: E
authors.initials: E
authors.lastname: Jakeman