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arXiv · 1710.05612

Ergodicity and Kolmogorov equations for dissipative SPDEs with singular drift: a variational approach

Carlo Marinelli·Luca Scarpa
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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 $L^1(μ)$ 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.

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Carlo Marinelli, Luca Scarpa. 2017-10-16. Ergodicity and Kolmogorov equations for dissipative SPDEs with singular drift: a variational approach. https://doi.org/10.1007/s11118-018-9731-5

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