Forward-convex convergence in probability of sequences of nonnegative random variables

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

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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:	30 Oct 2024 23:18
URI:	http://eprints.lse.ac.uk/id/eprint/85887

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