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Methodology and Computing in Applied Probability

, Volume 20, Issue 3, pp 1003–1012 | Cite as

Markov Property in Discrete Schur-constant Models

  • Claude Lefèvre
  • Stéphane Loisel
  • Sergey Utev
Article

Abstract

This paper is concerned with Schur-constant survival models for discrete random variables. Our main purpose is to prove that the associated partial sum process is a non-homogeneous Markov chain. This is shown in three different situations where the random variables considered take values in the sets 0, {0,1} or {0,…,m}, m ≥ 2. The property of Schur-constancy is also compared for these three cases.

Keywords

Schur-constancy property Discrete models Exchangeable random variables Non-homogeneous Markov chain 

Mathematics Subject Classification (2010)

60J10 62E10 

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Notes

Acknowledgments

We thank the referee for valuable comments and suggestions. C. L. received support from the Chair Generali Actuariat Responsable sponsored by the French Fondation du Risque. S. L. received support from the Research Project LoLitA of the French Agence Nationale de la Recherche, and the Chair Actuariat Durable sponsored by Milliman. The research of S. U. was funded by a Mission Scientifique of the Belgian FNRS.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Claude Lefèvre
    • 1
    • 2
  • Stéphane Loisel
    • 2
  • Sergey Utev
    • 3
  1. 1.Département de MathématiqueUniversité Libre de BruxellesBruxellesBelgium
  2. 2.Institut de Science Financière et d’AssurancesUniversité de LyonLyonFrance
  3. 3.Department of MathematicsUniversity of LeicesterLeicesterUK

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