Moments, continuity, and multifractal analysis of Mandelbrot martingales
Let Mandelbrot measure be a statistically self-similar measure \(\mu\) on the boundary of a \(c\)-ary tree, obtained by multiplying random weights indexed by the nodes of the tree. The author takes particular interest in the random variable \(Y=\|\mu\|\). He studies the existence of finite moments of negative orders for \(Y\), conditionally to \(Y>0\), and the continuity properties of \(Y\) with respect to the weights. These results on moments make it possible to study, with probability one, the existence of local Hölder exponent for \(\mu\), almost everywhere with respect to another Mandelbrot measure, as well as to perform the multifractal analysis of \(\mu\), under hypotheses that are weaker than those usually assumed.
scientific article; zbMATH DE number 1300445