Kardaras, Constantinos 
ORCID: 0000-0001-6903-4506 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 |
|---|---|
| Official URL: | http://www.ams.org/journals/proc |
| Additional Information: | © 2012 American Mathematical Society |
| Divisions: | Statistics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 30 Nov 2017 10:16 |
| Last Modified: | 12 Dec 2024 00:32 |
| URI: | http://eprints.lse.ac.uk/id/eprint/85887 |
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