A condition for the positivity of the density of an invariant measure
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.
scientific article; zbMATH DE number 5998403
scientific article