Stochastic order characterization of uniform integrability and tightness

Lasse Leskelä, Matti Vihola

Research output: Contribution to journalArticleScientificpeer-review

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. 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.
Original languageEnglish
Pages (from-to)382-389
Number of pages8
JournalStatistics and Probability Letters
Volume83
Issue number1
Publication statusPublished - 2013
MoE publication typeA1 Journal article-refereed

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