On the scaling function of multifractal processes

Benoit Mandelbrot, the father of Fractal Geometry, developed a multifractal model for describing price changes. Despite the commonly used models such as the Brownian motion, the Mutifractal Model of Asset Return (MMAR) takes into account scale-consistency, long-range dependence and heavy tails, thus having a great exibility in depicting the real-market peculiarities. In section 2 a review of the mathematics involved into multifractals is presented; Section 3 shows how to extend multifractality to stochastic processes. Contributions in Section 4 are new in the literature and extend Mandelbrot's results to canonical multifractal measures. Proof of Theorem 5 is unpublished and highlights which are the drivers of heavy tails in the process, thus possibly creating a bridge between multifractal formalism and jump processes.