Almost Sure Limit Points for Subsequences of Partial Sums

Abstract

Let {X_n, n ≥ 1} be a sequence of i. i. d. random variables with a common distribution function F. When F belongs to the domain of partial attraction of a Semi Stable law with index α, 0 < α < 2, we obtain almost sure limit points for subsequences of partial sums, along with some boundary crossing problems.