Tail and moment estimates for sums of independent random vectors with logarithmically concave tails
Volume 118 / 1996
Studia Mathematica 118 (1996), 301-304
DOI: 10.4064/sm-118-3-301-304
Abstract
Let $X_i$ be a sequence of independent symmetric real random variables with logarithmically concave tails. We consider a variable $X = ∑v_{i}X_{i}$, where $v_i$ are vectors of some Banach space. We derive approximate formulas for the tail and moments of ∥X∥. The estimates are exact up to some universal constant and they extend results of S. J. Dilworth and S. J. Montgomery-Smith [1] for the Rademacher sequence and E. D. Gluskin and S. Kwapień [2] for real coefficients.
