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Association of probability measures on partially ordered spaces

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  • Lindqvist, Bo Henry

Abstract

A notion of association of probability measures on partially ordered (Polish) spaces is introduced and its basic properties are investigated. This generalizes the classical notion of association among random variables, due to Esary, Proschan, and Walkup. The relation between association and monotone stochastic kernels is investigated and a theorem of Jogdeo is generalized. The general theory is applied to stochastic processes with both discrete and continuous time parameter and partially ordered state spaces. Also, an application to mixtures of statistical experiments is included.

Suggested Citation

  • Lindqvist, Bo Henry, 1988. "Association of probability measures on partially ordered spaces," Journal of Multivariate Analysis, Elsevier, vol. 26(2), pages 111-132, August.
    • Handle: RePEc:eee:jmvana:v:26:y:1988:i:2:p:111-132
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    Cited by:

    1. Cai, Jun & Li, Haijun, 2005. "Multivariate risk model of phase type," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 137-152, April.
    2. Colangelo, Antonio & Hu, Taizhong & Shaked, Moshe, 2008. "Conditional orderings and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 358-371, March.
    3. L. Dai & C. H. Chen, 1997. "Rates of Convergence of Ordinal Comparison for Dependent Discrete Event Dynamic Systems," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 29-54, July.
    4. Li, Haijun, 2003. "Association of multivariate phase-type distributions, with applications to shock models," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 381-392, October.
    5. Lirong Cui & Haijun Li, 2006. "Opportunistic Maintenance for Multi-component Shock Models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(3), pages 493-511, July.
    6. Li, Haijun & Xu, Susan H., 2001. "Stochastic Bounds and Dependence Properties of Survival Times in a Multicomponent Shock Model," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 63-89, January.
    7. Haijun Li & Susan H. Xu, 2004. "On the Coordinated Random Group Replacement Policy in Multivariate Repairable Systems," Operations Research, INFORMS, vol. 52(3), pages 464-477, June.
    8. Hofert, Marius & Vrins, Frédéric, 2013. "Sibuya copulas," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 318-337.
    9. Beate Sildnes & Bo Henry Lindqvist, 2018. "Modeling of semi-competing risks by means of first passage times of a stochastic process," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 153-175, January.
    10. Franco Pellerey & Cristina Zucca, 2005. "Stochastic Bounds for the Sparre Andersen Process," Methodology and Computing in Applied Probability, Springer, vol. 7(2), pages 225-247, June.
    11. Collet, Pierre & López, F. Javier & Martínez, Servet, 2003. "Order relations of measures when avoiding decreasing sets," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 165-175, November.

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