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.
Acknowledgement
The authors would like to thank Dmitry Dolgopyat for useful discussions and suggestions during the project and carefully reading the manuscript. C. Liverani acknowledges the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006.
Citation
Kasun Fernando. Carlangelo Liverani. "Edgeworth expansions for weakly dependent random variables." Ann. Inst. H. Poincaré Probab. Statist. 57 (1) 469 - 505, February 2021. https://doi.org/10.1214/20-AIHP1085
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