Marinelli, C;
Scarpa, L;
(2018)
Ergodicity and Kolmogorov Equations for Dissipative SPDEs with Singular Drift: a Variational Approach.
Potential Analysis
10.1007/s11118-018-9731-5.
(In press).
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Abstract
We prove existence of invariant measures for the Markovian semigroup generated by the solution to a parabolic semilinear stochastic PDE whose nonlinear drift term satisfies only a kind of symmetry condition on its behavior at infinity, but no restriction on its growth rate is imposed. Thanks to strong integrability properties of invariant measures μ, solvability of the associated Kolmogorov equation in L1(μ) is then established, and the infinitesimal generator of the transition semigroup is identified as the closure of the Kolmogorov operator. A key role is played by a generalized variational setting.
| Type: | Article |
|---|---|
| Title: | Ergodicity and Kolmogorov Equations for Dissipative SPDEs with Singular Drift: a Variational Approach |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s11118-018-9731-5 |
| Publisher version: | https://doi.org/10.1007/s11118-018-9731-5 |
| Language: | English |
| Additional information: | This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| Keywords: | Stochastic PDEs, Invariant measures, Ergodicity, Monotone operators |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10035271 |
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