Ornstein–Uhlenbeck equations with time-dependent coefficients and Lévy noise in finite and infinite dimensions

摘要

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.