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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 = ∑ 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.

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

Rafał Latała (1996)

Studia Mathematica

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.

The Poisson boundary of random rational affinities

Sara Brofferio (2006)

Annales de l’institut Fourier

We prove that in order to describe the Poisson boundary of rational affinities, it is necessary and sufficient to consider the action on real and all p -adic fileds.

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