Combining multifractal additive and multiplicative chaos

Combining multifractal additive and multiplicative chaos (2005)

by Julien Barral , Stéphane Seuret

Venue:	COMMUN. MATH. PHYS
Citations:	18 - 11 self

User correction supplied by mph

Datum	Value	Source
TITLE	Combining multifractal additive and multiplicative chaos	INFERENCE
AUTHOR NAME	Julien Barral	user correction
AUTHOR NAME	Stéphane Seuret	user correction
ABSTRACT	In this work, we study the new class of multifractal measures, which combines additive and multiplicative chaos, defined by νγ,σ = X b j≥1 −jγ j2 X 0 ≤ k ≤bj µ([kb −1 −j, (k + 1)b −j)) σ δkb−j (γ ≥ 0, σ ≥ 1), where µ is any positive Borel measure on [0, 1] and b is an integer ≥ 2. The singularities analysis of the measures νγ,σ involves new results on the mass distribution of µ when µ describes large classes of multifractal measures. These results generalize ubiquity theorems associated with the Lebesgue measure. Under suitable assumptions on µ, the multifractal spectrum of νγ,σ is linear on [0, hγ,σ] for some critical value hγ,σ, and then it is strictly concave on the right of hγ,σ, and deduced from the one of µ by an affine transformation. This untypical shape is the result of the combination between Dirac masses and atomless multifractal measures. These measures satisfy multifractal formalisms. These measures open interesting perspectives in modeling discontinuous phenomena.	user correction
YEAR	2005	INFERENCE
VENUE	COMMUN. MATH. PHYS	user correction
VENUE TYPE	JOURNAL	INFERENCE
PAGES	473--497	INFERENCE
CITATIONS	52 found	ParsCit 1.0