Quasi-Feller Markov chains. (2000)

• Record Type: Journal Article
• Authors: Lasserre, Jean B.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 13:Number 1(2000)
• Page Start: 15
• Page End: 24
• Publication Date: 2000
• Subjects: Markov chains -- Feller property -- weak convergences of measures; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953300000022
• Languages: English
• ISSNs: 1048-9533

Abstract

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.