Abstract
This paper considers Markov chains on a locally compact separable metricspace, which have an invariant probability measure but with no otherassumption on the transition kernel. Within this context, the limit providedby several ergodic theorems is explicitly identified in terms of the limitof the expected occupation measures. We also extend Yosida’s‘ergodic’ decomposition for Feller-like kernels to arbitrarykernels, and present ergodic results for empirical occupation measures, aswell as for additive-noise systems.
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Hernández-Lerma, O., Lasserre, J.B. Ergodic Theorems and Ergodic Decomposition for Markov Chains. Acta Applicandae Mathematicae 54, 99–119 (1998). https://doi.org/10.1023/A:1006012022894
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DOI: https://doi.org/10.1023/A:1006012022894