Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 1, Pages 15-24
doi:10.1155/S1048953300000022
Abstract
We consider the class of Markov kernels for which the weak or strong
Feller property fails to hold at some discontinuity set. We provide a simple necessary and sufficient condition for existence of an invariant probability measure as well as a Foster-Lyapunov sufficient condition. We also
characterize a subclass, the quasi (weak or strong) Feller kernels, for which
the sequences of expected occupation measures share the same asymptotic
properties as for (weak or strong) Feller kernels. In particular, it is shown
that the sequences of expected occupation measures of strong and quasi
strong-Feller kernels with an invariant probability measure converge setwise to an invariant measure.