Covariance identities and inequalities for functionals on Wiener and Poisson spaces (Q1897190)

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)].