A CASCADE DECOMPOSITION-THEORY WITH APPLICATIONS TO MARKOV AND EXCHANGEABLE CASCADES

A multiplicative random cascade refers to a positive T-martingale in t he sense of Kahane on the ultrametric space T = {0,1,...,b-1}(N). A ne w approach to the study of multiplicative cascades is introduced. The methods apply broadly to the problems of: (i) non-degeneracy criterion , (ii) dimension spectra of carrying sets, and (iii) divergence of mom ents criterion. Specific applications are given to cascades generated by Markov and exchangeable processes, as well as to homogeneous indepe ndent cascades.