Ornstein-Uhlenbeck equations with time-dependent coefficients and Lévy noise in finite and infinite dimensions (Q409209)

A time-dependent linear SPDE with additive Lévy noise in the mild and weak sense is investigated. Existence of a generalized invariant measure for the associated transition semigroup is established and the generator is studied on the corresponding \(L ^{2}\)-space. By characterizing the associated square field, a Poincaré and a Harnack inequality are derived. The main results are illustrated by some concrete examples.