Anomalous diffusion in correlated continuous time random walks

We demonstrate that continuous time randomwalks inwhich successivewaiting times are correlated by Gaussian statistics lead to anomalous diffusion with the mean squared displacement < r(2)(t) similar or equal to t(2/3). Long-ranged correlations of the waiting times with a power-law exponent alpha (0 < alpha <= 2) give rise to subdiffusion of the form < r(2)(t) similar or equal to t(alpha/(1+alpha)). In contrast, correlations in the jump lengths are shown to produce superdiffusion. We show that in both cases weak ergodicity breaking occurs. Our results are in excellent agreement with simulations.