Generalized continuous-time random walks, subordination by hitting times, and fractional dynamics

Functional limit theorems for continuous-time random walks (CTRW) are found in the general case of dependent waiting times and jump sizes that are also position dependent. The limiting anomalous diffusion is described in terms of fractional dynamics. Probabilistic interpretation of generalized fractional evolution is given in terms of the random time change (subordination) by means of hitting times processes