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Discussion Paper

Multifractal Products of Cylindrical Pulses

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.