Poincaré and log-Sobolev inequality for stationary Gaussian processes and moving average processes
type: Item
instance of: scholarly article
title: Poincaré and log-Sobolev inequality for stationary Gaussian processes and moving average processes
zbMATH Open document ID: 1090.60035
author: Guangfei Li
author: Yu Miao
author: Huiming Peng
author: Liming Wu
published in: Annales Mathématiques Blaise Pascal
publication date: 2006-03-29T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/10518
review text: Let \(X=(X_n)_{n\in\mathbb Z}\) be a real-valued stationary Gaussian process. The aim of the present paper is to characterize those processes \(X\) for which the Poincaré and/or the logarithmic Sobolev inequality hold in \(\mathbb R^{\mathbb Z}\). The characterization is in terms of the spectral measure \(\mu\) of \(X\). For example, \(X\) satisfies the above mentioned inequalities if and only if \(\mu\) is absolutely continuous with respect to the Lebesgue measure and, moreover, the density of \(\mu\) is bounded. The authors obtain also sharp bounds in these inequalities.
reviewed by: Werner Linde
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 5016090
zbMATH Keywords: Poincaré inequality
zbMATH Keywords: logarithmic Sobolev inequality
MaRDI profile type: Publication
OpenAlex ID: W2325621996
cites work: On bilinear forms in Gaussian random variables and Toeplitz matrices
cites work: Moderate deviations of empirical periodogram and non-linear functionals of moving average processes
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cites work: Q4938929
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cites work: Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
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DOI: 10.5802/AMBP.205
description: scientific article; zbMATH DE number 5016090