Positiveness of invariant measures of diffusion processes (Q2377516)

This short note studies measures \(\mu\) on \(\mathbb{R}^n\), which are solutions of \({\mathcal L}^* \mu\), where \({\mathcal L}\) is a linear second order differential operator. This means that for all smooth functions \(u\) one has \(\int Lu \;d\mu=0\). The main results of the paper give sufficient conditions that ensure the positivity of the density of \(\mu\).