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Tail and moment estimates for sums of independent random variables with logarithmically concave tails

E. Gluskin; S. Kwapień — 1995

Studia Mathematica

For random variables $S = \sum_{i = 1}^{\infty} α_{i} ξ_{i}$ , where $(ξ_{i})$ is a sequence of symmetric, independent, identically distributed random variables such that $l n P (| ξ_{i} | \geq t)$ is a concave function we give estimates from above and from below for the tail and moments of S. The estimates are exact up to a constant depending only on the distribution of ξ. They extend results of S. J. Montgomery-Smith [MS], M. Ledoux and M. Talagrand [LT, Chapter 4.1] and P. Hitczenko [H] for the Rademacher sequence.

A generalization of Khintchine's inequality and its application in the theory of operator ideals

E. Gluskin; A. Pietsch; J. Puhl — 1980

Studia Mathematica

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