Functional limit theorems for weighted sums of i.i.d. random variables (Q1059924)

Let \(\{X_ i\}\) be a sequence of independent and identically distributed random variables belonging to the domain of attraction of a stable law with index \(\alpha\), \(0<\alpha \leq 2\). The paper presents some functional limit theorems of the processes \(t\to \sum^{\infty}_{i=0}c_ i(\lambda; t)X_ i\) for some weights \(c_ i(\lambda; t)\), as \(\lambda\) \(\to \infty\). The basic idea of the approach to the problem is to use the so-called point-process method. Applications to the special weights concerning the classical summability methods such as Abel, Borel and Euler are given.