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A new isoperimetric inequality for product measure and the tails of sums of independent random variables. (English) Zbl 0760.60005

In [author, Ann. Probab. 17, No. 4, 1546-1570 (1989; Zbl 0692.60016)] a new method to study the tails of a sum of independent mean zero Banach- space valued random variables have been developed. The method was based on isoperimetric inequalities for product measure. In the paper under review a new isoperimetric inequality is proved and an improvement of the basic estimate of a tail of a sum of independent random variables from the previous paper is given.

MSC:

60B05 Probability measures on topological spaces
46B09 Probabilistic methods in Banach space theory

Citations:

Zbl 0692.60016
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References:

[1] W. Johnson, G. Schechtman, Remarks on Talagrand’s deviation inequality for Rademacher functions. Longhorn notes, Lecture Notes in Math, Springer Verlag, to appear. · Zbl 0753.60024
[2] S. Kwapien and J. Szulga, Hypercontraction methods for comparison of moments of random series in normed spaces. Ann. Probab, to appear.
[3] M. Ledoux, M. Talagrand, Some applications of isoperimetric methods to strong limit theorems for sums of independent random variables. Ann. Probab. 18 (1990), 754–789. · Zbl 0713.60005 · doi:10.1214/aop/1176990857
[4] M. Talagrand, An isoperimetric theorem on the cube and the Kintchine-Kahane inequalities. Proc. Amer. Mat. Soc. 104 (1988), 905–909. · Zbl 0691.60015 · doi:10.1090/S0002-9939-1988-0964871-7
[5] M. Talagrand, Isoperimetry and integrability of the sum of independent Banach-space valued random variables. Ann. Probab. 17 (1989), 1546–1570. · Zbl 0692.60016 · doi:10.1214/aop/1176991174
[6] M. Talagrand, Some isoperimetric inequalities and their applications, to appear in Proceedings of ICM, Kyoto (1990). · Zbl 0713.60005
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