Abstract
In this note we give simple proofs of some of the inequalities on Rademacher series given by M. Ledoux and M. Talagrand, [6], ch.4.1, S.J. Montgomery -Smith, [8], and by P. Hitczenko, [3]. We obtain better constants with proofs which can be useful in some other cases. As a corollary we prove a theorem of Kolmogorov on the lower estimates of the tail of sums of symmetric, independent random variables.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S.J. Dilworth and S.J. Montgomery-Smith, The distribution of vector-valued Rademacher series, Ann. Probab. 21 (1993), 2046–2052.
T. Figiel, P. Hitczenko, W.B. Johnson, G. Schechtman and J. Zinn, Extremal properties of Rademacher functions with applications to Khintchine and Rosenthal inequalities, in preparation.
P. Hitczenko, Domination inequality for martingale transforms of Rademacher sequence, Israel J. Math., 84 (1993), 161–178
S. Kwapień, Decoupling inequalities for polynomial chaos, Ann. Probab., 15 (1987), 1062–1071
S. Kwapień and W.A. Woyczyński, Random Series and Stochastic Integrals. Single and Multiple, Birkhäuser, Boston, 1992
M. Ledoux and M. Talagrand, Probability in Banach spaces, Springer-Verlag, 1991
A.W. Marshall and I. Olkin, Inequalities: Theory of Majorization and Its Applications, Academic Press, New York, 1979
S.J. Montgomery-Smith, The distribution of Rademacher sums, Proc. Amer. Math. Soc, 109 (1990), 517–522
I. Pinelis, Extremal probabilistic problems and Hotelling’s T 2 test under a symmetry condition, Ann. Statist., to appear
W. Stout, Almost sure convergence, Academic Press, New York, 1974
S.J. Szarek, On the best constant in the Khintchine inequality, Studia Math., 58 (1976), 197–208.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media New York
About this paper
Cite this paper
Hitczenko, P., Kwapień, S. (1994). On the Rademacher Series. In: Hoffmann-Jørgensen, J., Kuelbs, J., Marcus, M.B. (eds) Probability in Banach Spaces, 9. Progress in Probability, vol 35. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0253-0_2
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0253-0_2
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6682-2
Online ISBN: 978-1-4612-0253-0
eBook Packages: Springer Book Archive