Introduction 1. Harris recurrence 2. Stable increasing processes and Mittag Leffler processes 3. The main theorem 4. Proofs for subsection 3.1 -- sufficient condition 5. Proofs for subsection 3.1 -- necessary condition 6. Nummelin splitting in discrete time 7. Nummelin-like splitting for general continuous time Harris processes and proofs for subsection 3.3 Overview. Assumptions (H1)-(H6)