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Markov Property in Discrete Schur-constant Models

Author

Listed:
  • Claude Lefèvre

    (Université Libre de Bruxelles
    Université de Lyon)

  • Stéphane Loisel

    (Université de Lyon)

  • Sergey Utev

    (University of Leicester)

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.

Suggested Citation

  • Claude Lefèvre & Stéphane Loisel & Sergey Utev, 2018. "Markov Property in Discrete Schur-constant Models," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 1003-1012, September.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:3:d:10.1007_s11009-017-9564-5
    DOI: 10.1007/s11009-017-9564-5
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    References listed on IDEAS

    as
    1. Claude Lefèvre & Stéphane Loisel & Sergey Utev, 2017. "On finite exchangeable sequences and their dependence," Post-Print hal-01995790, HAL.
    2. Castañer, A. & Claramunt, M.M. & Lefèvre, C. & Loisel, S., 2015. "Discrete Schur-constant models," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 343-362.
    3. Chi, Yichun & Yang, Jingping & Qi, Yongcheng, 2009. "Decomposition of a Schur-constant model and its applications," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 398-408, June.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Claude Lefèvre & Matthieu Simon, 2021. "Schur-Constant and Related Dependence Models, with Application to Ruin Probabilities," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 317-339, March.
    2. Kolev, Nikolai & Mulinacci, Sabrina, 2022. "New characterizations of bivariate discrete Schur-constant models," Statistics & Probability Letters, Elsevier, vol. 180(C).
    3. Castañer, Anna & Claramunt, M. Mercè & Lefèvre, Claude & Loisel, Stéphane, 2019. "Partially Schur-constant models," Journal of Multivariate Analysis, Elsevier, vol. 172(C), pages 47-58.

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