Stochastic order characterization of uniform integrability and tightness
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 dominati...
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| Format: | Journal article |
| Language: | English |
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2013
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| _version_ | 1797095094674784256 |
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| author | Leskelä, L Vihola, M |
| author_facet | Leskelä, L Vihola, M |
| author_sort | Leskelä, L |
| collection | OXFORD |
| description | 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. © 2012 Elsevier B.V. |
| first_indexed | 2024-03-07T04:23:09Z |
| format | Journal article |
| id | oxford-uuid:cbb567fb-a62f-4060-a7cf-9fc637c1f58e |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:23:09Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | oxford-uuid:cbb567fb-a62f-4060-a7cf-9fc637c1f58e2022-03-27T07:16:45ZStochastic order characterization of uniform integrability and tightnessJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:cbb567fb-a62f-4060-a7cf-9fc637c1f58eEnglishSymplectic Elements at Oxford2013Leskelä, LVihola, MWe 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. © 2012 Elsevier B.V. |
| spellingShingle | Leskelä, L Vihola, M Stochastic order characterization of uniform integrability and tightness |
| title | Stochastic order characterization of uniform integrability and tightness |
| title_full | Stochastic order characterization of uniform integrability and tightness |
| title_fullStr | Stochastic order characterization of uniform integrability and tightness |
| title_full_unstemmed | Stochastic order characterization of uniform integrability and tightness |
| title_short | Stochastic order characterization of uniform integrability and tightness |
| title_sort | stochastic order characterization of uniform integrability and tightness |
| work_keys_str_mv | AT leskelal stochasticordercharacterizationofuniformintegrabilityandtightness AT viholam stochasticordercharacterizationofuniformintegrabilityandtightness |