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.

Ergodicity and Kolmogorov Equations for Dissipative SPDEs with Singular Drift: a Variational Approach

Scarpa L.
2020-01-01

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.
2020
Ergodicity
Invariant measures
Monotone operators
Stochastic PDEs
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1165477
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