Publication Date: January 2001
A new class of random multiplicative and statistically self-similar measures is defned on IR. It is the limit of measure-valued martingales constructed by multiplying random functions attached to the points of a statistically self-similar Poisson point process in a strip of the plane. Several fundamental problems are solved, including the non-degeneracy and the distribution of the limit measure, mu; the ﬁniteness of the (positive and negative) moments of the total mass of mu restricted to bounded intervals.
Compared to the familiar canonical multifractals generated by multiplicative cascades, the new measures and their multifractal analysis exhibit strikingly novel features which are discussed in detail.
Random measures, Multifractal analysis, Continuous time martingales, Statistically self-similar Poisson point processes
Published in Probability Theory and Related Fields (November 2002), 124(3): 409-430 [DOI]