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

100%

Gluskin E. D., Kwapień S.

Studia Mathematica

1995

tom 114

nr 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.

A generalization of Khintchine's inequality and its application in the theory of operator ideals

51%

Gluskin E. D., Pietsch A., Puhl J.

Studia Mathematica

1980

tom 67

nr 2

149-155

Ograniczanie wyników

2 Studia Mathematica

2 Gluskin E. D.

1 Kwapień S.

1 Pietsch A.

1 Puhl J.

1 1995

1 1980

Wyniki wyszukiwania

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

A generalization of Khintchine's inequality and its application in the theory of operator ideals