Abstract
AbstractFor discrete parameter Markov processes on a general state space, Birkhoff’s ergodic theorem provides a natural approach to the existence of invariant probabilities and the corresponding strong law of large numbers in some generality. In addition, it is shown that the notion of an irreducible positive recurrent Markov chain on a countable state space is equivalent to being irreducible ergodic stationary Markov chain having a unique invariant initial distribution.
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