Maximal inequalities for \(N\)-demimartingale and strong law of large numbers
type: Item
instance of: scholarly article
title: Maximal inequalities for \(N\)-demimartingale and strong law of large numbers
zbMATH Open document ID: 1223.60019
author: Shuhe Hu
author: B. L. S. Prakasa Rao
author: Wenzhi Yang
author: Xuejun Wang
published in: Statistics \& Probability Letters
publication date: 2011-07-26T00:00:00Z
review text: Let \(\{S_n,\, n\geq 1\}\) be an \(L^1\) sequence of random variables and suppose that \[ E[(S_{j+1}-S_j)f(S_1,\dots,S_j)] \leq 0 \] for all coordinatewise nondecreasing functions \(f\) for which the expectation is defined. Such a sequences \(\{S_n,\, n \geq 1\}\) is called a \(N\)-demimartingale [\textit{T. C. Christofides}, Arch. Inequal. Appl. 1, No. 3--4, 387--397 (2003; Zbl 1051.60021); \textit{B. L. S. Prakasa Rao}, J. Indian Soc. Agric. Stat. 57, Spec. Issue, Article No. 21, 208--216 (2004; Zbl 1188.60020)]. The authors derive some maximal inequalities for \(N\)-demimartingales. As applications of these inequalities, they prove a strong law of large numbers and obtain some related results.
reviewed by: B. L. S. Prakasa Rao
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 5932100
zbMATH Keywords: \(N\)-demimartingale
zbMATH Keywords: \(N\)-demisupermartingale
zbMATH Keywords: strong law of large numbers
zbMATH Keywords: growth rate
zbMATH Keywords: integrability of supremum
MaRDI profile type: Publication
full work available at URL: j.spl.2011.04.018
OpenAlex ID: W2071757577
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DOI: 10.1016/J.SPL.2011.04.018
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description: scientific article; zbMATH DE number 5932100