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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.

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 $X = \sum v_{i} X_{i}$ , 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 critical case of the Cramer-Lundberg theorem on the asymptotic tail behavior of the maximum of a negative drift random walk.

Korshunov, D.A. (2005)

Sibirskij Matematicheskij Zhurnal

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.

Currently displaying 1 – 20 of 36

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Displaying 1 – 20 of 36

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

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

Tail behaviour of multiple random integrals and $U$ -statistics.

Tauberian theorems for summability transforms.

Tecniche per risolvere problemi di Testa e Croce

The best bounds in a theorem of Russell Lyons.

The Beurling estimate for a class of random walks.

The convolution equation of Choquet and Deny for probability measures on discrete semigroups

The critical case of the Cramer-Lundberg theorem on the asymptotic tail behavior of the maximum of a negative drift random walk.

The determination of the spectral multiplicity of a stochastic process by RKHS method

The distribution of non-commutative Rademacher series.

The Green formula and HP Spaces on trees.

The growth exponent for planar loop-erased random walk.

The kernel method: a collection of examples.

The mass of sites visited by a random walk on an infinite graph.

The missing factor in Hoeffding's inequalities

The Poisson boundary of random rational affinities

The Pólya-Aeppli process and ruin problems.

The renewal theorem for random walk in two-dimensional time

The Resolvent for Simple Random Walks on the Free Product of Two Discrete Groups.

Currently displaying 1 – 20 of 36