  We study functionals of the form \[\zeta_{t}=\int_0^{t}...\int_0^{t} |
X_1(s_1)+...+ X_p(s_p)|^{-\sigma}ds_1... ds_p\] where $X_1(t),..., X_p(t)$ are
i.i.d. $d$-dimensional symmetric stable processes of index $0<\bb\le 2$. We
obtain results about the large deviations and laws of the iterated logarithm
for $\zeta_{t}$.
