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

E. GluskinS. Kwapień — 1995

Studia Mathematica

For random variables S = i = 1 α i ξ i , where ( ξ i ) is a sequence of symmetric, independent, identically distributed random variables such that l n P ( | ξ i | 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.

Unsolved Problems

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