Electronic Communications in Probability

A multivariate version of Hoeffding's inequality

Peter Major

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In this paper a multivariate version of Hoeffding's inequality is proved about the tail distribution of homogeneous polynomials of Rademacher functions with an optimal constant in the exponent of the upper bound. The proof is based on an estimate about the moments of homogeneous polynomials of Rademacher functions which can be considered as an improvement of Borell's inequality in a most important special case.

Article information

Electron. Commun. Probab., Volume 11 (2006), paper no. 24, 220-229.

Accepted: 9 October 2006
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60H05: Stochastic integrals

Hoeffding's inequality Borell's inequality multiple Wiener–It^o integrals diagram formula

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Major, Peter. A multivariate version of Hoeffding's inequality. Electron. Commun. Probab. 11 (2006), paper no. 24, 220--229. doi:10.1214/ECP.v11-1221. https://projecteuclid.org/euclid.ecp/1465058867

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