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Rhodes, Rémi; Sohier, Julien; Vargas, Vincent

Levy multiplicative chaos and star scale invariant random measures. (English) Zbl 1295.60064

Ann. Probab. 42, No. 2, 689-724 (2014).
In [Lect. Notes Phys. 12, 333–351 (1972; Zbl 0227.76081)], B. B. Mandelbrot built random measures describing energy dissipation and motivating intermittency effect in Kolmogorov’s theory of fully developed turbulence.
In the present paper, the authors study the solution to the continuous star equation (the celebrated star equation was introduced by B. Mandelbrot [C. R. Acad. Sci., Paris, Sér. A 278, 289–292 (1974; Zbl 0276.60096); ibid. 355–358 (1974; Zbl 0276.60097)]).
Reviewer: Sophia L. Kalpazidou (Thessaloniki)

Cited in 11 Documents

MSC:

60G57 Random measures
28A80 Fractals
60H25 Random operators and equations (aspects of stochastic analysis)
60G15 Gaussian processes
60G18 Self-similar stochastic processes

Keywords:

random measure; star equation; scale invariance; multiplicative chaos; uniqueness; infinitely divisible processes; multifractal processes; Mandelbrot star equation

Citations:

Zbl 0227.76081; Zbl 0276.60096; Zbl 0276.60097
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\textit{R. Rhodes} et al., Ann. Probab. 42, No. 2, 689--724 (2014; Zbl 1295.60064)
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