Gaussian Multiplicative Chaos revisited

Robert, Raoul; Vargas, Vincent

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

External document link

http://hal.archives-ouvertes.fr/hal-00293830/en/

Date

2010

Journal name

Annals of Probability

Volume

Number

Publisher

Institute of Mathematical Statistics

Pages

605-631

Abstract (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.

Subjects / Keywords

Multifractal processes; Random measures; Gaussian processes