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 generalized
superdiffusive regime is established. This is verified by showing that the
square width of the probability distribution (appropriately defined)grows as
t2/γ with 0<γ≤2 when t→∞. An important connection
of our results and those of Tsallis' nonextensive statistics is shown. The
normalized q-expectation value of x2 calculated with the corresponding
probability distribution behaves exactly as t2/γ in the asymptotic
limit.Comment: 9 pages (.tex file), 1 Postscript figures, uses revtex.st