Summary
Corresponding to anyp-functionp, a stationary version of the associated regenerative phenomenon is constructed for which the underlying “probability” measure may have infinite total mass (though it will always be σ-finite ifp is standard). As a trivial consequence,p is a positive-definite function. The construction is generalised to quasi-Markov chains.
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Kingman, J.F.C. Stationary regenerative phenomena. Z. Wahrscheinlichkeitstheorie verw Gebiete 15, 1–18 (1970). https://doi.org/10.1007/BF01041971
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DOI: https://doi.org/10.1007/BF01041971