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1997 | 123 | 1 | 15-42
Tytuł artykułu

Moment inequalities for sums of certain independent symmetric random variables

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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.
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  • Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205, U.S.A.
  • Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211, U.S.A.
  • Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
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