The Annals of Probability

Gaussian multiplicative chaos revisited

Raoul Robert and Vincent Vargas

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Abstract

In this article, we extend the theory of multiplicative chaos for positive definite functions in ℝd of the form f(x)=λ2ln+R/|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 [Ann. Sci. Math. Québec 9 (1985) 105–150]. As a main application, we provide a rigorous mathematical meaning to the Kolmogorov–Obukhov model of energy dissipation in a turbulent flow.

Article information

Source
Ann. Probab., Volume 38, Number 2 (2010), 605-631.

Dates
First available in Project Euclid: 9 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.aop/1268143528

Digital Object Identifier
doi:10.1214/09-AOP490

Mathematical Reviews number (MathSciNet)
MR2642887

Zentralblatt MATH identifier
1191.60066

Subjects
Primary: 60G57: Random measures 60G15: Gaussian processes 60G25: Prediction theory [See also 62M20] 28A80: Fractals [See also 37Fxx]

Keywords
Random measures Gaussian processes multifractal processes

Citation

Robert, Raoul; Vargas, Vincent. Gaussian multiplicative chaos revisited. Ann. Probab. 38 (2010), no. 2, 605--631. doi:10.1214/09-AOP490. https://projecteuclid.org/euclid.aop/1268143528


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