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Gaussian Multiplicative Chaos revisited

Robert, Raoul; Vargas, Vincent (2010), Gaussian Multiplicative Chaos revisited, Annals of Probability, 38, 2, p. 605-631. http://dx.doi.org/10.1214/09-AOP490

Type
Article accepté pour publication ou publié
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http://hal.archives-ouvertes.fr/hal-00293830/en/
Date
2010
Nom de la revue
Annals of Probability
Volume
38
Numéro
2
Éditeur
Institute of Mathematical Statistics
Pages
605-631
Identifiant publication
Métadonnées
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Auteur(s)
Robert, Raoul
Vargas, Vincent
Résumé (EN)
In this article, we extend the theory of multiplicative chaos for positive definite functions in Rd of the form f(x) = 2 ln+ T|x|+ g(x) where g is a continuous and bounded function. The construction is simpler and more general than the one defined by Kahane in 1985. As main application, we give a rigorous mathematical meaning to the Kolmogorov-Obukhov model of energy dissipation in a turbulent flow.
Mots-clés
Multifractal processes; Random measures; Gaussian processes