Bernoulli

  • Bernoulli
  • Volume 8, Number 6 (2002), 697-720.

Concentration and deviation inequalities in infinite dimensions via covariance representations

Christian Houdré and Nicolas Privault

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Abstract

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 $\{-1,1\}^\infty$.

Article information

Source
Bernoulli, Volume 8, Number 6 (2002), 697-720.

Dates
First available in Project Euclid: 9 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1076364802

Mathematical Reviews number (MathSciNet)
MR1962538

Zentralblatt MATH identifier
1012.60020

Keywords
chaotic representation property Clark formula concentration inequalities covariance identities deviation inequalities

Citation

Houdré, Christian; Privault, Nicolas. Concentration and deviation inequalities in infinite dimensions via covariance representations. Bernoulli 8 (2002), no. 6, 697--720. https://projecteuclid.org/euclid.bj/1076364802


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