A condition for the positivity of the density of an invariant measure. (English. Russian original) Zbl 1266.60121
Dokl. Math. 83, No. 3, 332-336 (2011); translation from Dokl. Akad. Nauk 438, No. 3, 295-299 (2011).
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.
Reviewer: Michael Scheutzow (Berlin)
MSC:
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 35J15 | Second-order elliptic equations |
| 35R06 | PDEs with measure |
References:
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