This article is cited in 1 paper

On Decoupling of Functions of Normal Vectors

P. G. Grigor'ev, S. A. Molchanov

University of North Carolina Charlotte, USA

Abstract: Two decoupling type inequalities for functions of Gaussian vectors are proved. In both cases, it turns out that the case of linear functions is the extreme one. The proofs involve certain properties of Wick's (Hermite's) polynomials and a refined version of Schur's theorem on entrywise product of positive definite matrices.

Keywords: decoupling, normally distributed random vector, Wick polynomial, Hermite polynomial, Schur product, Hadamard product, covariance matrix.

UDC: 519.213.22

Received: 01.07.2011

DOI: 10.4213/mzm9856

 English version: Mathematical Notes, 2012, 92:3, 362–368

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