Lévy multiplicative chaos and star scale invariant random structures

R. Rhodes, J. Sohier, V. Vargas

Research output: Contribution to journalArticleAcademicpeer-review

15 Citations (Scopus)
107 Downloads (Pure)


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 Lévy multiplicative chaos that generalizes the already existing constructions. Keywords: Random measure, star equation, scale invariance, multiplicative chaos, uniqueness, infinitely divisible processes, multifractal processes.
Original languageEnglish
Pages (from-to)689-724
Number of pages36
JournalThe Annals of Probability
Issue number2
Publication statusPublished - 2014


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