Lognormal star-scale invariant random measures
Allez, Romain; Rhodes, Rémi; Vargas, Vincent (2013), Lognormal star-scale invariant random measures, Probability Theory and Related Fields, 155, 3-4, p. 751-788. http://dx.doi.org/10.1007/s00440-012-0412-9
TypeArticle accepté pour publication ou publié
Journal nameProbability Theory and Related Fields
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Abstract (EN)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. We also prove that qualitative properties such as long-range independence or isotropy can be read off the equation.
Subjects / KeywordsScale invariance; Random measure; Multiplicative chaos; Star equation; Uniqueness
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