Contents Introduction p. 1 1. Harris recurrence p. 7 2. Stable increasing processes and Mittag Leffier processes p. 17 3. The main theorem p. 22 3.1 Processes with life cycles p. 23 3.2 Examples p. 27 3.3 General Harris processes p. 32 4. Proofs for subsection 3.1 - sufficient condition p. 34 5. Proofs for subsection 3.1 - necessary condition p. 47 6. Nummelin splitting in discrete time p. 62 7. Nummelin-like splitting for general continuous time Harris processes and proofs for subsection 3.3 p. 67 Overview: assumptions (HI) - (H6) p. 86 References p. 88 v
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