On distributionally regenerative Markov chains (Q1965897)

A variant on the notion of distributional regeneration in a general Markov chain is introduced. It is related to recurrent stochastic matrices with countable index sets. A minorization inequality for the dual operator of a transition kernel is shown to be a sufficient condition for the distributional regenerativity. It is also employed in a characterization of the positive recurrence. The results are illustrated on shifts over finite alphabets and on \(S\)-unimodal interval maps.