Stochasticity and fractalityin irregular space plasmas

One of the most relevant feature of turbulent fluids, included Space Plasmas, is the irregularity of the fields defining their local state (for example $\vec{B}$, $\vec{j}$ and $\vec{v}$ in the Solar Wind). In particular, time series of local quantities collected by \emph{in situ} measurements, e.g. by satellites, as well as remote sensing data, e.g. those from trans-medium communications, show scale-dependent statistical behaviour suggesting the local state fields to be better represented as \emph{fractal} or \emph{multi-fractal measures} rather than smooth functions of time and position.
In this presentation, the relationship between those measured fractal properties and the stochastic generalizations of fluid models describing the plasma is traced, suggesting a possible future development of Space Plasma turbulence theory.