A condition for the positivity of the density of an invariant measure
type: Item
instance of: scholarly article
title: A condition for the positivity of the density of an invariant measure
zbMATH Open document ID: 1266.60121
DOI: 10.1134/S1064562411030185
author: B. V. Agafontsev
author: Vladimir I. Bogachev
author: S. V. Shaposhnikov
published in: Doklady Mathematics
publication date: 2012-01-17T00:00:00Z
review text: Suppose that \(\mu\) is an invariant probability measure on \(\mathbb{R}^d\) associated to an elliptic operator \(L\) with drift \(b\). The authors show that under rather general assumptions an additional integrability condition on \(b\) with respect to \(\mu\) suffices to conclude that \(\mu\) has a strictly positive density \(\rho\). They also provide an explicit lower bound for \(\rho(x)\). Finally they prove a corresponding local result.
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 35R06
zbMATH DE Number: 5998403
zbMATH Keywords: invariant measure
zbMATH Keywords: elliptic operator
zbMATH Keywords: positive density
reviewed by: Michael Scheutzow
MaRDI profile type: Publication
cites work: ON REGULARITY OF TRANSITION PROBABILITIES AND INVARIANT MEASURES OF SINGULAR DIFFUSIONS UNDER MINIMAL CONDITIONS
cites work: Elliptic and parabolic equations for measures
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cites work: Differentiable measures and the Malliavin calculus
cites work: Q3579316
cites work: Exponential divergence estimates and heat kernel tail.
cites work: Density minoration of a strongly non-degenerated random variable
full work available at URL: s1064562411030185
OpenAlex ID: W1986309373
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description: scientific article; zbMATH DE number 5998403