On moment conditions for the supremum of normed sums
type: Item
instance of: scholarly article
title: On moment conditions for the supremum of normed sums
zbMATH Open document ID: 0631.60014
DOI: 10.1016/0304-4149(87)90053-6
author: Bong Dae Choi
author: Soo Hak Sung
published in: Stochastic Processes and their Applications
publication date: 1987-01-01T00:00:00Z
review text: The main result: Let \((X_ n)_{n\geq 1}\) be a sequence of random variables and \(c_ n\), \(n\geq 1\), constants with \(0<c_ n\to \infty\). If \(\sum_{n}E| X_ n|^{\alpha \beta}/c_ n^{\beta}<\infty\) for some \(\beta >1\) and \(0<\alpha \beta <2\), then \[ E\quad (\sup_{n}| \sum_{k\leq n}(X_ k-\alpha_ k)|^{\alpha}/c_ n)<\infty \] where \(\alpha_ k=0\) if \(0<\alpha \beta \leq 1\) and \(\alpha_ k=E(X_ k| X_ 1,...,X_{k-1})\) if \(1<\alpha \beta \leq 2\). This result is applied to the special case of i.i.d. \(X_ n's\).
reviewed by: M.P.Jerschow
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 60G42
zbMATH DE Number: 4026430
zbMATH Keywords: maximal inequality
zbMATH Keywords: martingale difference
zbMATH Keywords: Bahr and Esseen inequality
MaRDI profile type: Publication
full work available at URL: 0304-4149(87)90053-6
OpenAlex ID: W1983123524
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description: scientific article; zbMATH DE number 4026430