an:05493467
Zbl 1173.35048
Shaposhnikov, S. V.
Positiveness of invariant measures of diffusion processes
EN
Dokl. Math. 76, No. 1, 533-538 (2007); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 415, No. 2, 174-179 (2007).
00231953
2007
j
35J25 35R05 60H15 35J15
positivity of solutions; invariant measures; linear PDE; second order
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 \(\mu\).
Dirk Bl??mker (Augsburg)