Multifractal products of cylindrical pulses

By J. Barral, Benoit B. Mandelbrot. 2002

204 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/75a59cfd89b692c31c716143b644288909dcef97

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Citations in the corpus

Critical Gaussian multiplicative chaos: Convergence of the derivative martingale (2012, background): “2 below for a quick reminder or [7, 11] for details.”
Heterogeneous ubiquitous systems in ℝd and Hausdorff dimension (2007, unknown): “In [7], it is shown that θ(1) > 0 is a necessary and sufficient condition for μ to be almost surely a positive measure supported by [0, 1).”
The singularity spectrum of Lévy processes in multifractal time (2007, background): “Other examples are the compound Poisson cascades and other R+-martingales studied in [5,6,10].”
KPZ formula for log-infinitely divisible multifractal random measures (2008, methodology): “Since ψ(−q) <∞, by using the same argument than the proof of theorem 3 (Moments of negative orders) in [3], one can show that: sup l′ E [ 1 ( ∫ 3T/4 T/4 e μ ( Al′(u)\(Al′ (0)∪Al′(T ) ) du )q ] <∞.”
Gaussian multiplicative chaos and applications: A review (2013, methodology): “There has been several works in this direction [12, 21, 63, 127], each of which focuses on a specific situation that is of interest for some given property.”
Wavelet construction of Generalized Multifractional processes. (2007, methodology): “2) For analyzing the irregularity of a signal {X(t)}t∈Rd having a very erratic pointwise Hölder exponent, one often uses some multifractal spectrum of {X(t)}t∈Rd, for example the singularities spectrum {θX(γ)}γ∈[0,1] which is a measure of the geometric repartition of the pointwise Hölder exponents o”
From Multifractal Measures to Multifractal Wavelet Series (2005, methodology): “For instance, Quasi-Bernoulli measures [16, 21, 23, 36], Mandelbrot cascades [41], compound Poisson cascade measures [9] and stable Lévy measures [14] belong to this class.”