Journal of Statistical Physics, Vol. 58, Nos. 5/6, 1990, p. 1267-1273.
We present some asymptotic results for the family of pausing time densities having the asymptotic (t->oo) property F(t)~ [tln^(1+gamma)(t/T)]^(-1). In particular, we show that for this class of pausing time densities the mean-squared displacement is asymptotically proportional to ln^gamma(t/T), and the asymptotic distribution of the displacement has a negative exponential form.