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Moment inequalities for sums of certain independent symmetric random variables

P. HitczenkoS. Montgomery-SmithK. Oleszkiewicz — 1997

Studia Mathematica

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 ) = e x p ( - 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.

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