Kardaras, Constantinos and Žitković, Gordan
(2013)
*Forward-convex convergence in probability of sequences of nonnegative random variables.*
Proceedings of the American Mathematical Society, 141 (3).
pp. 919-929.
ISSN 0002-9939

Identification Number: 10.1090/S0002-9939-2012-11373-5

## Abstract

For a sequence $ (f_n)_{n \in \mathbb{N}}$ of nonnegative random variables, we provide simple necessary and sufficient conditions for convergence in probability of each sequence $ (h_n)_{n \in \mathbb{N}}$ with $ h_n\in \mathrm {conv}(\{f_n,f_{n+1},\dots \})$ for all $ n \in \mathbb{N}$ to the same limit. These conditions correspond to an essentially measure-free version of the notion of uniform integrability.

Item Type: | Article |
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Official URL: | http://www.ams.org/journals/proc |

Additional Information: | © 2012 American Mathematical Society |

Divisions: | Statistics |

Subjects: | Q Science > QA Mathematics |

Sets: | Departments > Statistics |

Date Deposited: | 30 Nov 2017 10:16 |

Last Modified: | 20 May 2019 01:35 |

URI: | http://eprints.lse.ac.uk/id/eprint/85887 |

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