Superdiffusion in decoupled continuous time random walks

Continuous time random walk models with decoupled waiting time density are studied. When the spatial one-jump probability density belongs to the Levy distribution type and the total time transition is exponential a generalize d superdiffusive regime is established. This is verified by showing that th e square width of the probability distribution (appropriately defined) grow s as t(2/gamma) with 0 < gamma less than or equal to 2 when t --> infinity. An important connection of our results and those of Tsallis' nonextensive statistics is shown. The normalized q-expectation value of x(2) calculated with the corresponding probability distribution behaves exactly as t(2/gamm a) in the asymptotic limit. (C) 2001 Elsevier Science B.V. All rights reser ved.