Let be a sequence of independent symmetric real random variables with logarithmically concave tails. We consider a variable , where 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.
@article{bwmeta1.element.bwnjournal-article-smv118i3p301bwm,
author = {Rafa\l\ Lata\l a},
title = {Tail and moment estimates for sums of independent random vectors with logarithmically concave tails},
journal = {Studia Mathematica},
volume = {119},
year = {1996},
pages = {301-304},
zbl = {0847.60031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv118i3p301bwm}
}
Latała, Rafał. Tail and moment estimates for sums of independent random vectors with logarithmically concave tails. Studia Mathematica, Tome 119 (1996) pp. 301-304. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv118i3p301bwm/
[00000] [1] S. J. Dilworth and S. J. Montgomery-Smith, The distribution of vector-valued Rademacher series, Ann. Probab. 21 (1993), 2046-2052. | Zbl 0798.46006
[00001] [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. | Zbl 0834.60050
[00002] [3] P. Hitczenko and S. Kwapień, On the Rademacher series, in: Probability in Banach Spaces 9, Birkhäuser, Boston, 31-36. | Zbl 0822.60013
[00003] [4] B. Maurey, Some deviation inequalities, Geom. Funct. Anal. 1 (1991), 188-197. | Zbl 0756.60018
[00004] [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. | Zbl 0818.46047