Illinois Journal of Mathematics, Volume (58), No (2), Year (2014-10) , Pages (561-575)

Title : ( Noncommutative Martingale Concentration Inequalities )

Authors: Ghadir Sadeghi , Mohammad Sal Moslehian ,
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Abstract

WeestablishanAzumatypeinequalityunderaLipshitzconditionformartingalesintheframeworkofnoncommutativeprobabilityspacesandapplyittodeduceanoncommutative HeoffdinginequalityaswellasanoncommutativeMcDiarmid typeinequality.WealsoprovideanoncommutativeAzumainequalityfornoncommutativesupermartingalesinwhichinstead ofafixedupperboundforthevarianceweassumethatthevarianceisboundedabovebyalinearfunctionofvariables.Wethen employittodeduceanoncommutativeBernsteininequalityand aninequalityinvolvingLp-normofthesumofamartingaledifference.

Keywords

, noncommutative, probability space, Azuma inequality, supermartingales
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@article{paperid:1048659,
author = {Ghadir Sadeghi and Sal Moslehian, Mohammad},
title = {Noncommutative Martingale Concentration Inequalities},
journal = {Illinois Journal of Mathematics},
year = {2014},
volume = {58},
number = {2},
month = {October},
issn = {0019-2082},
pages = {561--575},
numpages = {14},
keywords = {noncommutative; probability space; Azuma inequality; supermartingales},
}

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%0 Journal Article
%T Noncommutative Martingale Concentration Inequalities
%A Ghadir Sadeghi
%A Sal Moslehian, Mohammad
%J Illinois Journal of Mathematics
%@ 0019-2082
%D 2014

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