Open Access
December 2002 Concentration and deviation inequalities in infinite dimensions via covariance representations
Christian Houdré, Nicolas Privault
Author Affiliations +
Bernoulli 8(6): 697-720 (December 2002).


Concentration and deviation inequalities are obtained for functionals on Wiener space, Poisson space or more generally for normal martingales and binomial processes. The method used here is based on covariance identities obtained via the chaotic representation property, and provides an alternative to the use of logarithmic Sobolev inequalities. It enables the recovery of known concentration and deviation inequalities on the Wiener and Poisson space (including those given by sharp logarithmic Sobolev inequalities), and extends results available in the discrete case, i.e. on the infinite cube $\{-1,1\}^\infty$.


Download Citation

Christian Houdré. Nicolas Privault. "Concentration and deviation inequalities in infinite dimensions via covariance representations." Bernoulli 8 (6) 697 - 720, December 2002.


Published: December 2002
First available in Project Euclid: 9 February 2004

zbMATH: 1012.60020
MathSciNet: MR1962538

Keywords: chaotic representation property , Clark formula , Concentration inequalities , covariance identities , Deviation inequalities

Rights: Copyright © 2002 Bernoulli Society for Mathematical Statistics and Probability

Vol.8 • No. 6 • December 2002
Back to Top