Abstract
In this chapter we consider the class of MCs on a LCS metric space X that have either the weak-or the strong-Feller property introduced in ¡ì4.4 (see Definition 4.4.2). The Feller property is a continuity property on the t.p.f. P of the MC. In particular, it permits to derive simple necessary and/or sufficient conditions for existence of an invariant p.m. for P (recall that most results in the previous chapters assumed that the MC had an invariant p.m.). In fact, most conditions for existence of an invariant p.m. do assume the weak-Feller property, and as can be shown in simple examples, the failure to satisfy this continuity condition can have important consequences (see, e.g., the MC defined by (7.3.1) below).
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© 2003 Springer Basel AG
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Herná-Lerma, O., Lasserre, J.B. (2003). Feller Markov Chains. In: Markov Chains and Invariant Probabilities. Progress in Mathematics, vol 211. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8024-4_7
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DOI: https://doi.org/10.1007/978-3-0348-8024-4_7
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9408-1
Online ISBN: 978-3-0348-8024-4
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