Pawel Hitczenko, Stephen Montgomery-Smith and Krzysztof Oleszkiewicz, Moment inequalities for sums of certain independent symmetric random variables.
Studia Math. 123, (1997), 15-42.
This paper gives upper and lower bounds for moments of sums of independent random variables \((X_k)\) which satisfy the condition that \(P(|X_k| > t) = \exp(-N_k(t))\), 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 \(0 < r \le 1\). This complements work of Gluskin and Kwapien who have done the same for convex functions \(N\).
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