Lognormal scale invariant random measures
Résumé
In this article, we consider the continuous analog of the celebrated Mandelbrot star equation with lognormal weights. We show existence and uniqueness of measures satisfying the aforementioned continuous equation; these measures fall under the scope of the Gaussian multplicative chaos theory developped by J.P. Kahane in 1985 (or possibly extensions of this theory). As a by product, we also obtain an explicit characterization of the covariance structure of these measures.
Domaines
Probabilités [math.PR]Origine | Fichiers produits par l'(les) auteur(s) |
---|