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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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