Moment inequalities for sums of certain independent symmetric random variables
Volume 123 / 1997
Studia Mathematica 123 (1997), 15-42
DOI: 10.4064/sm-123-1-15-42
Abstract
This paper gives upper and lower bounds for moments of sums of independent random variables $(X_k)$ which satisfy the condition $P(|X|_k ≥ t) = exp(-N_k(t))$, where $N_k$ are concave functions. As a consequence we obtain precise information about the tail probabilities of linear combinations of independent random variables for which $N(t) = |t|^r$ for some fixed 0 < r ≤ 1. This complements work of Gluskin and Kwapień who have done the same for convex functions N.
