The domain of partial attraction of an infinitely divisible law without a normal component (Q1902812)

Working within the framework of Csörgö, Haeusler and Mason's `probabilistic approach' to the asymptotic distribution of sums of independent and identically distributed random variables, we completely characterize the domain of partial attraction of infinitely divisible distributions without a normal component. It turns out that an attracting distribution with a finite Lévy measure arises along subsequences of the positive integers in two qualitatively different ways, depending on whether a certain parameter associated with the measure is less than or greater than one. This dichotomy resolves an earlier indeterminacy in the overall characterization.