Asymptotic behavior of strong Feller semigroups

Abstract

We prove that a weakly ergodic, strong Feller semigroup on the space of measures converges strongly to a projection onto its fixed space. In contrast to a recent result of Gerlach we do not assume the semigroup to be stochastically continuous.

Withdrawn, due to mistake in the proof of Theorem 3.1

References in corpus (3)

• A Pettis-Type Integral and Applications to Transition Semigroups
• A new proof of Doob's theorem
• On the lattice structure of weakly continuous operators on the space of measures