A Φ-Entropy Contraction Inequality for Gaussian Vectors

Liming Wu ()
Additional contact information
Liming Wu: Université Blaise Pascal

Journal of Theoretical Probability, 2009, vol. 22, issue 4, 983-991

Abstract: Abstract A beautiful result of Sarmanov (Dokl. Akad. Nauk SSSR 121(1), 52–55, 1958) says that for a Gaussian vector (X,Y), $\operatorname {Var}(\mathbb {E}[f(Y)|X])\le \rho^{2}\operatorname {Var}(f(Y))$ for all measurable functions f, where ρ is the (linear) correlation coefficient between X and Y. We generalize this result to a general Φ-entropy (a nonlinear version of his result) by means of a previous result of D. Chafai based on Bakry–Emery’s Γ 2-technique and tensorization.

Keywords: Gaussian vectors; Φ-entropy; 60E15; 60G15; 39B62 (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-009-0211-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:22:y:2009:i:4:d:10.1007_s10959-009-0211-0

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-009-0211-0

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().