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Invariant probabilities for Markov chains on a metric space

✍ Scribed by Jean B. Lasserre

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
317 KB
Volume
34
Category
Article
ISSN
0167-7152

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✦ Synopsis

We consider Markov kernels on a locally compact separable metric space that satisfy the (weak) Feller property. We provide a very simple necessary and sufficient condition for existence of an invariant probability measure. We also prove that every Feller Markov kernel on a compact Hausdorff (not necessarily metric) has an invariant probability measure. An alternative sample-path critcrion of existence is also provided, as well as a sufficient condition for uniqueness.

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