A Random Process for the Construction of Multiaffine Fields

We define a random process for the construction of multiaffine fields, given the scaling exponents for the structure functions. The difference with analogous processes for positive defined multifractal measures is stressed. In particular our methods can be used for the study of the scaling laws exhibited by the velocity field in three dimensional fully developed turbulence. We also discuss the probability distribution functions for the increments of the signal in the scaling range