Some Results on Small-Deviation Probability Convergence Rates for Sums of Independent Random Variables

Abstract

Let ﹛X j ,j = 1, 2, 3, …﹜ be a sequence of independent, non-degenerate random variables and write Under quite a diverse variety of conditions we may obtain as n → ∞ for all x, — ∞ < x < ∞, and some real p ⩾ 0. For example, suppose the ﹛X j ﹜ happen to be distributed identically and belong to the domain of normal attraction of a symmetric stable law with characteristic exponent α, 0 < α ⩽ < 2, α ≠ 1.