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A Gaussian expectation product inequality
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
Ningbo University of Technology, Peoples R China.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
2017 (English)In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 124Article in journal (Refereed) Published
Abstract [en]

Let (X-1,. . ., X-n) be any n-dimensional centered Gaussian random vector, in this note the following expectation product inequality is proved: E Pi (n)(j=1) f(j)( X-j) amp;gt;= Pi (n)(j=1) Ef(j)(X-j) for functionsh, 1 amp;lt;= j amp;lt;= n, taking the forms f(j)(x) = integral(infinity)(0) where mu(j), 1 amp;lt;= j amp;lt;= n, are finite positive measures. The motivation of studying such an inequality comes from the Gaussian correlation conjecture (which was recently proved) and the Gaussian moment product conjecture (which is still unsolved). Several explicit examples of such functions f(j) are given. The proof is built on characteristic functions of Gaussian random variables. (C) 2017 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE BV , 2017. Vol. 124
Keyword [en]
Gaussian random vector; Bochners theorem; Gaussian expectation product inequality
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-136567DOI: 10.1016/j.spl.2016.12.018ISI: 000395210700001OAI: oai:DiVA.org:liu-136567DiVA: diva2:1090314
Available from: 2017-04-24 Created: 2017-04-24 Last updated: 2017-04-24

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