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Matematicheskie Zametki, 2012, Volume 92, Issue 3, Pages 401–409
DOI: https://doi.org/10.4213/mzm9856 (Mi mzm9856) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On Decoupling of Functions of Normal Vectors

P. G. Grigor'ev, S. A. Molchanov

University of North Carolina Charlotte, USA
Full-text PDF (450 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm9856
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.
Received: 01.07.2011
English version:
Mathematical Notes, 2012, Volume 92, Issue 3, Pages 362–368
DOI: https://doi.org/10.1134/S0001434612090088
Bibliographic databases:
Document Type: Article
UDC: 519.213.22
Language: Russian
Citation: P. G. Grigor'ev, S. A. Molchanov, “On Decoupling of Functions of Normal Vectors”, Mat. Zametki, 92:3 (2012), 401–409; Math. Notes, 92:3 (2012), 362–368
Citation in format AMSBIB
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