Multifractal decomposition of statistically self-similar sets (Q5946551)

In this paper under review, the authors investigate the multifractal spectrum of certain random measure on a statistically self-similar set \(K\) defined by \textit{S. Graf} [Probab. Theory Relat. Fields 74, 357-392 (1987; Zbl 0591.60005)]. Their main result extends those of \textit{R. Cawley} and \textit{R. D. Mauldin} [Adv. Math. 92, No. 2, 196-236 (1992; Zbl 0763.58018)] for deterministic Moran fractals and \textit{K. J. Falconer} [J. Theor. Probab. 7, No. 3, 681-702 (1994; Zbl 0805.60034)] by allowing different contraction ratios for the similarity mappings in the iterative construction procedure.