Moment inequalities for sums of certain independent symmetric random variables

• Autorzy: P. Hitczenko , S. J. Montgomery-Smith , K. Oleszkiewicz
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 60G50: Sums of independent random variables; random walks
• 60E15: Inequalities; stochastic orderings

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 123
• Numer: 1
• Strony: 15-42

Daty

wydano

1997

otrzymano

1995-11-07

poprawiono

1996-07-17

Twórcy

autor

P. Hitczenko

• Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205, U.S.A.

autor

S. J. Montgomery-Smith

• Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211, U.S.A.

autor

K. Oleszkiewicz

• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Bibliografia

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