Renewal representations for Markov operators

AbstractAs is known, due to the existence of an embedded renewal structure, the iterates of a Harris recurrent Markov operator can be represented as a (delayed) renewal sequence. We show that these kind of representations also exist for a larger class of Markov operators, provided only that certain “filling schemes” are “successful.” As applications of the theory we study the co-Feller operators and Markov operators which “contract the variation.