Ornstein-Uhlenbeck Equations with time-dependent coefficients and Levy Noise in finite and infinite dimensions

We solve a time-dependent linear SPDE with additive Levy noise in the mild and weak sense. Existence of a generalized invariant measure for the associated transition semigroup is established and the generator is characterized on the corresponding L^2-space. The square field operator is calculated, allowing to derive a Poincare and a Harnack inequality.