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Order relations of measures when avoiding decreasing sets

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  • Collet, Pierre
  • López, F. Javier
  • Martínez, Servet

Abstract

We consider a discrete-time ergodic Markov chain on a partially ordered state space and study the stochastic comparison between its invariant measure and some measures related with the behaviour of the chain conditioned to avoid a decreasing subset of the state space. We also study the situation when several decreasing sets are avoided.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:65:y:2003:i:3:p:165-175
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    References listed on IDEAS

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    1. José Moler & Fernando Plo & Miguel Miguel, 2000. "Minimal quasi-stationary distributions under nullR-recurrence," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 455-470, December.
    2. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 467-498, December.
    3. Lindqvist, Bo Henry, 1988. "Association of probability measures on partially ordered spaces," Journal of Multivariate Analysis, Elsevier, vol. 26(2), pages 111-132, August.
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    Cited by:

    1. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2006. "Some positive dependence stochastic orders," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 46-78, January.

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