Summary.
Given a closed Markov (i.e. regenerative) set in [0,∞), we characterize the laws of the Markov sets which are regeneratively embedded into the latter. Typically, let Φ(1) and Φ(2) be two Laplace exponents corresponding to two regenerative laws, and M (2) a Markov set with exponent Φ(2). There exists a Markov set M (1) with exponent Φ(1) which is regeneratively embedded into M (2) if and only if Φ(1)/Φ(2) is a completely monotone function. Several examples and applications are discussed.
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Received: 12 April 1996 / In revised form: 12 March 1997
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Bertoin, J. Regenerative embedding of Markov sets. Probab Theory Relat Fields 108, 559–571 (1997). https://doi.org/10.1007/s004400050121
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DOI: https://doi.org/10.1007/s004400050121