Stochastic order characterization of uniform integrability and tightness

Details Stochastic order characterization of uniform integrability and tightness Stochastic order characterization of uniform integrability and tightness

2011-06-03

arxiv.org/abs/1106.0607v1

Mathematics

Probability

14 pages, 1 figure

Scientific paper

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. Especially, 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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