Large deviations for martingales.
type: Item
instance of: scholarly article
title: Large deviations for martingales.
zbMATH Open document ID: 1059.60033
DOI: 10.1016/S0304-4149(01)00112-0
author: Emmanuel Lesigne
author: Dalibor Volný
published in: Stochastic Processes and their Applications
publication date: 2005-02-25T00:00:00Z
review text: The authors present new large deviations results for partial sums of martingale differences. Provided boundedness of an exponential moment they prove optimality of the estimate \(\text{e}^{-cn^{1/3}}\) instead of the estimate \(\text{e}^{-cn}\) known for the i.i.d.\ case. Provided boundedness of a \(p\)th moment (\(p\geq 2\)) they show optimality of an estimate \(cn^{-p/2}\) instead of the estimate \(cn^{1-p}\) known for the i.i.d.\ case. Similar results are also derived for a martingale difference field.
reviewed by: Petr Lachout
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60G42
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 60G10
zbMATH DE Number: 2138907
zbMATH Keywords: large deviations
zbMATH Keywords: independent random variables
zbMATH Keywords: martingale difference sequence
zbMATH Keywords: martingale difference field
zbMATH Keywords: stationary random variables
zbMATH Keywords: stationary random fields
MaRDI profile type: Publication
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full work available at URL: s0304-4149(01)00112-0
OpenAlex ID: W1979459108
description: scientific article; zbMATH DE number 2138907