This article describes a versatile family of functions increasingly roughened by successive interpolations. They provide models of the variation of financial prices. More importantly, they are helpful "cartoons" of Brownian motions in multifractal time, BMMT, which are better models described in...

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...