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

Studia Mathematica (1996)

- Volume: 118, Issue: 3, page 301-304
- ISSN: 0039-3223

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topLatała, Rafał. "Tail and moment estimates for sums of independent random vectors with logarithmically concave tails." Studia Mathematica 118.3 (1996): 301-304. <http://eudml.org/doc/216280>.

@article{Latała1996,

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.},

author = {Latała, Rafał},

journal = {Studia Mathematica},

keywords = {tail and moment estimates; logarithmically concave tails; Rademacher sequence},

language = {eng},

number = {3},

pages = {301-304},

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

url = {http://eudml.org/doc/216280},

volume = {118},

year = {1996},

}

TY - JOUR

AU - Latała, Rafał

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

JO - Studia Mathematica

PY - 1996

VL - 118

IS - 3

SP - 301

EP - 304

AB - 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.

LA - eng

KW - tail and moment estimates; logarithmically concave tails; Rademacher sequence

UR - http://eudml.org/doc/216280

ER -

## References

top- [1] S. J. Dilworth and S. J. Montgomery-Smith, The distribution of vector-valued Rademacher series, Ann. Probab. 21 (1993), 2046-2052. Zbl0798.46006
- [2] E. D. Gluskin and S. Kwapień, Tail and moment estimates for sums of independent random variables with logarithmically concave tails, Studia Math. 114 (1995), 303-309. Zbl0834.60050
- [3] P. Hitczenko and S. Kwapień, On the Rademacher series, in: Probability in Banach Spaces 9, Birkhäuser, Boston, 31-36. Zbl0822.60013
- [4] B. Maurey, Some deviation inequalities, Geom. Funct. Anal. 1 (1991), 188-197. Zbl0756.60018
- [5] M. Talagrand, A new isoperimetric inequality and the concentration of measure phenomenon, in: Israel Seminar (GAFA), Lecture Notes in Math. 1469, Springer, 1991, 94-124. Zbl0818.46047

## Citations in EuDML Documents

top- 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
- Radosław Adamczak, Rafał Latała, Tail and moment estimates for chaoses generated by symmetric random variables with logarithmically concave tails

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