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

Studia Mathematica (1995)

- Volume: 114, Issue: 3, page 303-309
- ISSN: 0039-3223

## Access Full Article

top## Abstract

top## How to cite

topGluskin, E., and Kwapień, S.. "Tail and moment estimates for sums of independent random variables with logarithmically concave tails." Studia Mathematica 114.3 (1995): 303-309. <http://eudml.org/doc/216194>.

@article{Gluskin1995,

abstract = {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.},

author = {Gluskin, E., Kwapień, S.},

journal = {Studia Mathematica},

keywords = {tail and moment estimates; sums of symmetric i.i.d. random variables; logarithmically concave tails; Rademacher sequence},

language = {eng},

number = {3},

pages = {303-309},

title = {Tail and moment estimates for sums of independent random variables with logarithmically concave tails},

url = {http://eudml.org/doc/216194},

volume = {114},

year = {1995},

}

TY - JOUR

AU - Gluskin, E.

AU - Kwapień, S.

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

JO - Studia Mathematica

PY - 1995

VL - 114

IS - 3

SP - 303

EP - 309

AB - 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.

LA - eng

KW - tail and moment estimates; sums of symmetric i.i.d. random variables; logarithmically concave tails; Rademacher sequence

UR - http://eudml.org/doc/216194

ER -

## References

top- [B] E. Berger, Majorization, exponential inequalities and almost sure behavior of vector valued random variables, Ann. Probab. 19 (1990), 1206-1226. Zbl0757.60002
- [H] P. Hitczenko, Domination inequality for martingale transforms of Rademacher sequences, Israel J. Math. 84 (1993), 161-178. Zbl0781.60037
- [HK] P. Hitczenko and S. Kwapień, On the Rademacher series, in: Probability in Banach Spaces, Proc. 9th Internat. Conf., Sandbjerg, 1993, Birkhäuser, 1994, 31-36. Zbl0822.60013
- [K] J.-P. Kahane, Some Random Series of Functions, Heath, 1968. Zbl0192.53801
- [KR] M. A. Krasnosel'skiĭ and Ya. B. Rutickiĭ, Convex Functions and Orlicz Spaces, Noordhoff, Groningen, 1961.
- [KW] S. Kwapień and W. Woyczyński, Random Series and Stochastic Integrals: Single and Multiple, Birkhäuser, 1992. Zbl0751.60035
- [LT] M. Ledoux and M. Talagrand, Probability in Banach Spaces, Springer, 1991. Zbl0748.60004
- [MO] A. W. Marshall and I. Olkin, Inequalities: Theory of Majorization and Its Applications, Academic Press, New York, 1979. Zbl0437.26007
- [MS] S. J. Montgomery-Smith, The distribution of Rademacher sums, Proc. Amer. Math. Soc. 109 (1990), 517-522. Zbl0696.60013

## Citations in EuDML Documents

top- Rafał Latała, Tail and moment estimates for sums of independent random vectors with logarithmically concave tails
- Miguel A. Arcones, The large deviation principle for certain series
- Miguel A. Arcones, The large deviation principle for certain series
- Rafał Latała, Tail and moment estimates for some types of chaos
- P. Hitczenko, S. Montgomery-Smith, K. Oleszkiewicz, Moment inequalities for sums of certain independent symmetric random variables
- Radosław Adamczak, Rafał Latała, Tail and moment estimates for chaoses generated by symmetric random variables with logarithmically concave tails

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.