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Stochastic order characterization of uniform integrability and tightness

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 betwee...

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Publisher copy:
10.1016/j.spl.2012.09.023

Authors


Leskelä, L More by this author
Journal:
Statistics and Probability Letters
Volume:
83
Issue:
1
Pages:
382-389
Publication date:
2013-01-05
DOI:
ISSN:
0167-7152
URN:
uuid:cbb567fb-a62f-4060-a7cf-9fc637c1f58e
Source identifiers:
487891
Local pid:
pubs:487891

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