Parametric Subordination in Fractional Diffusion Processes

The purpose of this chapter is to describe our method of parametric subordination to produce particle trajectories for the so-called fractional diffusion processes. By replacing in the common diffusion equation the first-order time derivative and the second-order space derivative by appropriate fractional derivatives, we obtain a fractional diffusion equation whose solution describes the temporal evolution of the density of an extensive quantity, e.g., of the sojourn probability of a diffusing particle.