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Stochastic order characterization of uniform integrability and tightness

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  • Leskelä, Lasse
  • Vihola, Matti
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    Abstract

    We show that a family of random variables is uniformly integrable if and only if it is stochastically bounded in the increasing convex order by an integrable random variable. This result is complemented by proving analogous statements for the strong stochastic order and for power-integrable dominating random variables. In particular, we show that, whenever a family of random variables is stochastically bounded by a p-integrable random variable for some p>1, there is no distinction between the strong order and the increasing convex order. These results also yield new characterizations of relative compactness in Wasserstein and Prohorov metrics.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 83 (2013)
    Issue (Month): 1 ()
    Pages: 382-389

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    Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:382-389

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    Related research

    Keywords: Strong stochastic order; Increasing convex order; Stochastic domination; Bounded in probability; Hardy–Littlewood maximal random variable;

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