On the generation of log-Lévy distributions and extreme randomness

Iddo Eliazar, Joseph Klafter

Research output: Contribution to journalArticlepeer-review

Abstract

The log-normal distribution is prevalent across the sciences, as it emerges from the combination of multiplicative processes and the central limit theorem (CLT). The CLT, beyond yielding the normal distribution, also yields the class of Lévy distributions. The log-Lévy distributions are the Lévy counterparts of the log-normal distribution, they appear in the context of ultraslow diffusion processes, and they are categorized by Mandelbrot as belonging to the class of extreme randomness. In this paper, we present a natural stochastic growth model from which both the log-normal distribution and the log-Lévy distributions emerge universallythe former in the case of deterministic underlying setting, and the latter in the case of stochastic underlying setting. In particular, we establish a stochastic growth model which universally generates Mandelbrots extreme randomness.

Original languageEnglish
Article number415003
JournalJournal of Physics A: Mathematical and Theoretical
Volume44
Issue number41
DOIs
StatePublished - 14 Oct 2011

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