Continuous time random walk models for fractional space-time diffusion equations

In this paper continuous time random walk models approximating fractional space-time diffusion processes are studied. Stochastic processes associated with the considered equations represent time-changed processes, where the time-change process is a L\'evy's stable subordinator with the stability index $\beta \in (0,1).$ In the parer the convergence of constructed CTRWs to time-changed processes associated with the corresponding fractional diffusion equations are proved using a new analytic method.