Multifractal analysis of complex random cascades

Abstract

We achieve the multifractal analysis of a class of complex valued statistically self-similar continuous functions. For we use multifractal formalisms associated with pointwise oscillation exponents of all orders. Our study exhibits new phenomena in multifractal analysis of continuous functions. In particular, we find examples of statistically self-similar such functions obeying the multifractal formalism and for which the support of the singularity spectrum is the whole interval $[0,\infty ]$.

37 pages, 8 figures

References in corpus (3)

• Log-infinitely divisible multifractal processes
• Convergence of complex multiplicative cascades
• Random wavelet series based on a tree-indexed Markov chain

Cited by in corpus (8)

• Exact dimensionality and projections of random self-similar measures and sets
• Critical Mandelbrot Cascades
• Convergence of complex multiplicative cascades
• Hausdorff and packing spectra, large deviations, and free energy for branching random walks in ${\mathbb{R}}^d$
• Uniform convergence for complex $[0,1]$-martingales
• Box-counting dimension in one-dimensional random geometry of multiplicative cascades
• Multifractal analysis of Gaussian multiplicative chaos and applications
• Noise-like analytic properties of imaginary chaos