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

Volume 114 / 1995

E. D. Gluskin Studia Mathematica 114 (1995), 303-309 DOI: 10.4064/sm-114-3-303-309


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 $ln P(|ξ_i| ≥ t)$ 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.


  • E. D. Gluskin

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