Discrete random walk models for symmetric Lévy–Feller diffusion processes

We propose a variety of models of random walk, discrete in space and time, suitable for simulating stable random variables of arbitrary index α (0<α 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 which we refer to as Lévy–Feller diffusion processes.