  We propose a variety of models of random walk, discrete in space and time,
suitable for simulating stable random variables of arbitrary index $\alpha$
($0< \alpha \le 2$), in the symmetric case. We show that by properly scaled
transition to vanishing space and time steps our random walk models converge to
the corresponding continuous Markovian stochastic processes, that we refer to
as Levy-Feller diffusion processes.
