On probability and moment inequalities for dependent random variables
type: Item
instance of: scholarly article
zbMATH Open document ID: 0981.60005
DOI: 10.1137/S0040585X97978142
publication date: 2001-10-22T00:00:00Z
Mathematics Subject Classification ID: 60E10
zbMATH DE Number: 1665909
zbMATH Keywords: Banach space
zbMATH Keywords: Gaussian random vector
zbMATH Keywords: Hilbert space
zbMATH Keywords: quantile
zbMATH Keywords: uniform mixing coefficient
zbMATH Keywords: Hoffmann-Jorgensen inequality
zbMATH Keywords: Marcinkiewicz-Zygmund inequality
zbMATH Keywords: Euler function
MaRDI profile type: Publication
full work available at URL: s0040585x97978142
OpenAlex ID: W2070318408
title: On probability and moment inequalities for dependent random variables
author: S. V. Nagaev
published in: Theory of Probability and its Applications
review text: Let \(X_k\), \(k= 1,\dots, n\), be a sequence of random variables with values in a separable Banach space with a norm. Set \(S_k= \sum^k_1 X_i\) and \(M_n= \max_{1<k<n}|S_k|\). The author modifies an inequality of \textit{J. Hoffmann-Jørgensen} [``Probability in B-spaces.'' Lecture Notes Series. No. 48. Aarhus: Aarhus Universitet, Matematisk Institut (1977; Zbl 0358.60002)] to obtain an upper estimate for the probability \(P\{M_n> r\}\).
reviewed by: Andreas N. Philippou
description: scientific article; zbMATH DE number 1665909