Ergodic Theorems and Ergodic Decomposition for Markov Chains

摘要

This paper considers Markov chains on a locally compact separable metric space, which have an invariant probability measure but with no other assumption on the transition kernel. Within this context, the limit provided by several ergodic theorems is explicitly identified in terms of the limit of the expected occupation measures. We also extend Yosida's 'ergodic' decomposition for Feller-like kernels to arbitrary kernels, and present ergodic results for empirical occupation measures, as well as for additive-noise systems.