Summary An integral analogue of the general almost sure limit theorem is presented. In the theorem, instead of a sequence of random elements, a continuous time random process is involved, moreover, instead of the logarithmical average, the integral of delta-measures is considered. Then the general theorem is applied to obtain almost sure versions of limit theorems for semistable and max-semistable processes, moreover for processes being in the domain of attraction of a stable law or being in the domain of geometric partial attraction of a semistable or a max-semistable law.
PITMAN, J. and YOR, M., Bessel processes and infinitelydivisiblelaws, Stochastic integrals (Proc. Sympos., Univ. Durham, Durham, 1980), ed. by D. Williams, Lecture Notes in Math., 851, Springer, Berlin, 1981. MR 82j :60149