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Regenerative embedding of Markov sets
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  • Published: August 1997

Regenerative embedding of Markov sets

  • Jean Bertoin1 

Probability Theory and Related Fields volume 108, pages 559–571 (1997)Cite this article

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  • 18 Citations

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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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Authors and Affiliations

  1. Laboratoire de Probabilités, Université Pierre et Marie Curie, 4, Place Jussieu, F-75252 Paris Cedex 05, France, , , , , , FR

    Jean Bertoin

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  1. Jean Bertoin
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Received: 12 April 1996 / In revised form: 12 March 1997

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Cite this article

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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  • Issue Date: August 1997

  • DOI: https://doi.org/10.1007/s004400050121

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  • Key words: Markov set
  • Regenerative property
  • Skorohod embedding
  • Subordinator.
  • Mathematics Subject Classification (1991): 60D05
  • 60J30
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