The graph, range and level set singularity spectra of $b$-adic independent cascade function

Abstract

With the "iso-H\"older" sets of a function we naturally associate subsets of the graph, range and level set of the function. We compute the associated singularity spectra for a class of statistically self-similar multifractal functions, namely the $b$-adic independent cascade function.Comment: 37 pages, 10 figure