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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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 http://www.ams.org/journals/proc © 2012 American Mathematical Society Statistics Q Science > QA Mathematics 30 Nov 2017 10:16 20 Oct 2021 03:18 http://eprints.lse.ac.uk/id/eprint/85887