Simple stochastic models showing strong anomalous diffusion

We show that strong anomalous diffusion, i.e. 〈|x(t)|q〉∼tqν(q) where qν(q) is a nonlinear function of q, is a generic phenomenon within a class of generalized continuous-time random walks. For such class of systems it is possible to compute analytically ν(2n) where n is an integer number. The presence of strong anomalous diffusion implies that the data collapse of the probability density function P(x,t)=t−ν(x/tν) cannot hold, a part (sometimes) in the limit of very small x/tν now ν=limq→0ν(q). Moreover the comparison with previous numerical results shows that the shape of F(x/tν) is not universal, i.e., one can have systems with the same ν but different F.