Continuity of the Multifractal Spectrum of a Random Statistically Self-Similar Measure

75 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Multifractal products of cylindrical pulses (2002, methodology): “To see that q � µq (Ca) is almost surely positive on J � for every a ∈ A ,s o that the support of the ˜ µq ’s is ∂A, adapt the proof of Corollary 5 (ii) (β) of [ B2 ] by using Theorem 5 and Eqs.”
The singularity spectrum of Lévy processes in multifractal time (2007, methodology): “non-trivial solution is given by the Laplace transform of the probability distribution of kµWk, where µW is an independent multiplicative cascade on [0,1] generated by the random vector W = (W0,...,Wb 1) used in (1), see [31,26] and Section 7 for the construction of µW. This type of multiplicative c”
Heterogeneous ubiquitous systems in ℝd and Hausdorff dimension (2007, background): “The multifractal nature of μ or of variants of μ has been investigated in many works [32, 27, 21, 38, 1, 37, 4].”
Gaussian multiplicative chaos and applications: A review (2013, background): “Nowadays, there is a huge amount of literature on multifractal analysis and it is far beyond the scope of this review to cite or discuss all the related mathematical achievements (in the case of Mandelbrot’s multiplicative cascades see [14, 15, 22] and references therein).”