The fluctuation behavior of the row sums in a triangular array of Poisson distributed random variables is described by the law of the iterated logarithm under two different assumptions of independence within the array. The results are applied to a sequence of Poisson random variables.

In a multi-type continuous time Markov branching process the asymptotic distribution of the first birth in and the last death (extinction) of the kth generation can be determined from the asymptotic behavior of the probability generating function of the vector Z(k)(t), the size of the kth...