Berkes, I., CÁki, E., Csörgö, S. and Megyesi, Z., Almostsurelimittheorems for sums and maxima from the domain of geometrical partial attraction of semistable laws, in: Limit theorems in probability and
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.
A certain class of stochastic summability methods of mantissa type is introduced and its connection to almost sure limit theorems
is discussed. The summability methods serve as suitable weights in almost sure limit theory, covering all relevant known examples
for, e.g., normalized sums or maxima of i.i.d. random variables. In the context of semistable domains of attraction the methods
lead to previously unknown versions of semistable almost sure limit theorems.
The problem of random allocation is that of placing
balls independently with equal probability to
boxes. For several domains of increasing numbers of balls and boxes, the final number of empty boxes is known to be asymptotically either normally or Poissonian distributed. In this paper we first derive a certain two-index transfer theorem for mixtures of the domains by considering random numbers of balls and boxes. As a consequence of a well known invariance principle this enables us to prove a corresponding general almost sure limit theorem. Both theorems inherit a mixture of normal and Poisson distributions in the limit. Applications of the general almost sure limit theorem for logarithmic weights complement and extend results of Fazekas and Chuprunov  and show that asymptotic normality dominates.
Summary Some topics of our twenty some years of joint work is discussed. Just to name a few; joint behavior of the maximum of the Wiener process and its location, global and local almost sure limit theorems, strong approximation of the planar local time difference, a general Strassen type theorem, maximal local time on subsets.
LANZINGER, H., An almostsurelimittheorem for moving averages of random variables between the strong law of large numbers and Erdös-Rényi law, ESAIM Probab. & Statist . 2 (1998), 163-183.
An almostsurelimittheorem for moving