Generalized scaling in nonscaling diffusion

Scaling diffusion r2(t) tα is usually observed only as an asymptotic for large or for small times t. Using a toy model it is shown that for intermediate times (when the scaling relationship r2(t) tα does not take place) the generalized scaling rp(t) r(t) χ(p) can still take place and χ(p)=pγ. It is also shown that for α>1 (in the large time asymptotic) the exponent γ increases with α in the interval 1 γ 2.