Levy multiplicative chaos and star scale invariant random measures
Abstract
In this article, we consider the continuous analog of the celebrated Mandelbrot star equation with infinitely divisible weights. Mandelbrot introduced this equation to characterize the law of multiplicative cascades. We show existence and uniqueness of measures satisfying the aforementioned continuous equation. We obtain an explicit characterization of the structure of these measures, which reflects the constraints imposed by the continuous setting. In particular, we show that the continuous equation enjoys some specific properties that do not appear in the discrete star equation. To that purpose, we define a L\'{e}vy multiplicative chaos that generalizes the already existing constructions.
Keywords
Cite
@article{arxiv.1201.5219,
title = {Levy multiplicative chaos and star scale invariant random measures},
author = {Rémi Rhodes and Julien Sohier and Vincent Vargas},
journal= {arXiv preprint arXiv:1201.5219},
year = {2014}
}
Comments
Published in at http://dx.doi.org/10.1214/12-AOP810 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)