The Annals of Probability
- Ann. Probab.
- Volume 42, Number 2 (2014), 689-724.
Levy multiplicative chaos and star scale invariant random measures
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.
Ann. Probab., Volume 42, Number 2 (2014), 689-724.
First available in Project Euclid: 24 February 2014
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Rhodes, Rémi; Sohier, Julien; Vargas, Vincent. Levy multiplicative chaos and star scale invariant random measures. Ann. Probab. 42 (2014), no. 2, 689--724. doi:10.1214/12-AOP810. https://projecteuclid.org/euclid.aop/1393251300