Abstract
We solve a time-dependent linear SPDE with additive Lévy noise in the mild and weak sense. Existence of a generalized invariant measure for the associated transition semigroup is established and the generator is studied on the corresponding L 2-space. The square field operator is characterized, allowing to derive a Poincaré and a Harnack inequality.
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Knäble, F. Ornstein–Uhlenbeck equations with time-dependent coefficients and Lévy noise in finite and infinite dimensions. J. Evol. Equ. 11, 959–993 (2011). https://doi.org/10.1007/s00028-011-0120-4
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DOI: https://doi.org/10.1007/s00028-011-0120-4