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Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 1, Pages 15-24

Quasi-Feller Markov chains

LAAS-CNRS, 7 A v. du Colonel Roche, Toulouse Cédex 4 31077, France

Received 1 October 1998; Revised 1 October 1999

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.