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Title: | Edgeworth expansions for weakly dependent random variables |
Authors: | Fernando, K Liverani, C |
Keywords: | Edgeworth expansions;expanding maps;Markov chains;weak dependence |
Issue Date: | 1-Feb-2021 |
Publisher: | Institute of Mathematical Statistics and Association des Publications de l’Institut Henri Poincaré |
Citation: | Fernando, K. and Liverani, C. (2021) 'Edgeworth expansions for weakly dependent random variables', Annales de l'institut Henri Poincare (B) Probability and Statistics, 57 (1), pp. 469 - 505. doi: 10.1214/20-AIHP1085. |
Abstract: | We discuss sufficient conditions that guarantee the existence of asymptotic expansions for the CLT for weakly dependent random variables including observations arising from sufficiently chaotic dynamical systems like piece-wise expanding maps, and strongly ergodic Markov chains. As a corollary we obtain refinements of the Local Limit Theorem and moderate deviation results. We primarily use spectral techniques to obtain the results. Nous discutons des conditions suffisantes garantissant l’existence d’expansions asymptotiques du théorème central limite pour des variables aléatoires faiblement dépendantes, dont des observations provenant de systèmes dynamiques suffisamment chaotiques comme des applications dilatantes par morceaux, et des chaînes de Markov fortement ergodiques. Comme corollaire, nous obtenons des raffinements du théorème local limite et de résultats de déviations modérées. Nos méthodes sont principalement des techniques spectrales. |
URI: | https://bura.brunel.ac.uk/handle/2438/27865 |
DOI: | https://doi.org/10.1214/20-AIHP1085 |
ISSN: | 0246-0203 |
Other Identifiers: | ORCID iD: Kasun Fernando |
Appears in Collections: | Dept of Mathematics Research Papers |
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FullText.pdf | Copyright © 2021 Association des Publications de l’Institut Henri Poincaré. All rights reserved. This is the publisher's peer reviewed, version of record made available on this institutional repository for personal use. No commercial reuse is permitted. The article is available online at: https://doi.org/10.1214/20-AIHP1085 . | 678.82 kB | Adobe PDF | View/Open |
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