We present a variety of models of random walk, discrete in space and time, suitable for simulating random variables whose probability density obeys a space–time fractional diffusion equation.

We propose a variety of models of random walk, discrete in space and time, suitable for simulating stable random variables of arbitrary index α (0α⩽2), in the symmetric case. We show that by properly scaled transition to vanishing space and time steps our random walk models converge to the...