A strong law of large numbers for martingale arrays

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dc.creatorAtchade, Yves F.
dc.date2009-05-17
dc.date.accessioned2026-07-07T13:15:57Z
dc.date.available2026-07-07T13:15:57Z
dc.descriptionWe prove a martingale triangular array generalization of the Chow-Birnbaum-Marshall's inequality. The result is used to derive a strong law of large numbers for martingale triangular arrays whose rows are asymptotically stable in a certain sense. To illustrate, we derive a simple proof, based on martingale arguments, of the consistency of kernel regression with dependent data. Another application can be found in \cite{atchadeetfort08} where the new inequality is used to prove a strong law of large numbers for adaptive Markov Chain Monte Carlo methods.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/0905.2761
dc.identifierhttp://arxiv.org/abs/0905.2761
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/230638
dc.subjectProbability
dc.subjectStatistics Theory
dc.subject60F15, 60G42
dc.titleA strong law of large numbers for martingale arrays
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