Concentration inequalities for upper probabilities

Abstract In this paper, we obtain a Bernstein-type concentration inequality and McDiarmid’s inequality under upper probabilities for exponential independent random variables. Compared with the classical result, our inequalities are investigated under a family of probability measures, rather than one...

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Main Author:	Yuzhen Tan
Format:	Article
Language:	English
Published:	SpringerOpen 2020-06-01
Series:	Journal of Inequalities and Applications
Subjects:	Concentration inequality Law of large numbers Upper probability Sublinear expectation
Online Access:	http://link.springer.com/article/10.1186/s13660-020-02417-6

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spelling	doaj-e1a0f6f098b24010afb60472cae753762020-11-25T02:48:17ZengSpringerOpenJournal of Inequalities and Applications1029-242X2020-06-012020111410.1186/s13660-020-02417-6Concentration inequalities for upper probabilitiesYuzhen Tan0Zhongtai Securities Institute for Financial Studies, Shandong UniversityAbstract In this paper, we obtain a Bernstein-type concentration inequality and McDiarmid’s inequality under upper probabilities for exponential independent random variables. Compared with the classical result, our inequalities are investigated under a family of probability measures, rather than one probability measure. As applications, the convergence rates of the law of large numbers and the Marcinkiewicz–Zygmund-type law of large numbers about the random variables in upper expectation spaces are obtained.http://link.springer.com/article/10.1186/s13660-020-02417-6Concentration inequalityLaw of large numbersUpper probabilitySublinear expectation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Yuzhen Tan
spellingShingle	Yuzhen Tan Concentration inequalities for upper probabilities Journal of Inequalities and Applications Concentration inequality Law of large numbers Upper probability Sublinear expectation
author_facet	Yuzhen Tan
author_sort	Yuzhen Tan
title	Concentration inequalities for upper probabilities
title_short	Concentration inequalities for upper probabilities
title_full	Concentration inequalities for upper probabilities
title_fullStr	Concentration inequalities for upper probabilities
title_full_unstemmed	Concentration inequalities for upper probabilities
title_sort	concentration inequalities for upper probabilities
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1029-242X
publishDate	2020-06-01
description	Abstract In this paper, we obtain a Bernstein-type concentration inequality and McDiarmid’s inequality under upper probabilities for exponential independent random variables. Compared with the classical result, our inequalities are investigated under a family of probability measures, rather than one probability measure. As applications, the convergence rates of the law of large numbers and the Marcinkiewicz–Zygmund-type law of large numbers about the random variables in upper expectation spaces are obtained.
topic	Concentration inequality Law of large numbers Upper probability Sublinear expectation
url	http://link.springer.com/article/10.1186/s13660-020-02417-6
work_keys_str_mv	AT yuzhentan concentrationinequalitiesforupperprobabilities
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Concentration inequalities for upper probabilities

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