Covariance identities and inequalities for functionals on Wiener and Poisson spaces
type: Item
instance of: scholarly article
title: Covariance identities and inequalities for functionals on Wiener and Poisson spaces
zbMATH Open document ID: 0831.60029
author: Christian Houdré
author: Víctor Pérez-Abreu
published in: The Annals of Probability
publication date: 1996-02-11T00:00:00Z
review text: The authors prove covariance identities and inequalities for functionals of the Wiener process and of the Poisson process using Malliavin calculus techniques. The results extend earlier inequalities for the variance of a function of a normal random variable obtained by \textit{H. Chernoff} [Ann. Probab. 9, 533-535 (1981; Zbl 0457.60014)], \textit{J. Nash} [Am. J. Math. 80, 931-954 (1958; Zbl 0096.069)] and others which in turn is a special case of a general Poincaré-type inequality for log concave densities given by \textit{H. J. Brascamp} and \textit{E. H. Lieb} [J. Funct. Anal. 22, 366-389 (1976; Zbl 0334.26009)].
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 60H07
zbMATH DE Number: 796548
zbMATH Keywords: covariance identities
zbMATH Keywords: inequalities for functionals of the Wiener process
zbMATH Keywords: Malliavin calculus techniques
reviewed by: B. L. S. Prakasa Rao
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176988392
OpenAlex ID: W1984582610
DOI: 10.1214/AOP/1176988392
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description: scientific article; zbMATH DE number 796548