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Powers and Products of Regenerative Phenomena

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Summary

The simultaneous occurrence of two independent regenerative phenomena defines a third, whose p-function is the product of the first two. Thus integer powers of p-functions are p-functions. The corresponding result for non-integer powers (with exponent α > 1) has been proved for discrete time phenomena and for standard continuous time phenomena. There are still open questions, notably whether the class of Markov p-functions is closed under non-integer powers. These questions are addressed by means of a new technique which relates the atoms of the canonical measure to ‘kinks’ in the p-function. This provides new information even for products of p-functions.
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Keywords: kink analysis; non-integer powers; p-functions; regenerative phenomena

Document Type: Research Article

Affiliations: Isaac Newton Institute for Mathematical Sciences, Cambridge, UK

Publication date: March 1, 2004

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