Levy multiplicative chaos and star scale invariant random measures
Sohier, Julien; Vargas, Vincent; Rhodes, Rémi (2014), Levy multiplicative chaos and star scale invariant random measures, Annals of Probability, 42, 2, p. 689-724. http://dx.doi.org/10.1214/12-AOP810
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-00662375
Journal nameAnnals of Probability
Institute of Mathematical Statistics
MetadataShow full item record
Abstract (EN)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 Levy multiplicative chaos that generalizes the already existing constructions.
Subjects / Keywordsmultifractal processes; infinitely divisible processes; multiplicative chaos; uniqueness
Showing items related by title and author.