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Positiveness of invariant measures of diffusion processes. (English. Russian original) Zbl 1173.35048
Dokl. Math. 76, No. 1, 533-538 (2007); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 415, No. 2, 174-179 (2007).
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 \(\mu\).
MSC:
35J25 Boundary value problems for second-order elliptic equations
35R05 PDEs with low regular coefficients and/or low regular data
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35J15 Second-order elliptic equations
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