Supremum of an even moment of sums of independent random variables
type: Item
instance of: scholarly article
title: Supremum of an even moment of sums of independent random variables
zbMATH Open document ID: 0731.60014
DOI: 10.1007/BF00970172
author: E. V. Bestsennaya
author: S. A. Utev
published in: Siberian Mathematical Journal
publication date: 1991-01-01T00:00:00Z
review text: The main result gives the following Theorem: For every integer \(m>1\), \[ \sup E(X_ 1+...+X_ n)^{2m}=\phi^{2m}E(\eta_{\lambda}- \lambda)^{2m}, \] where the supremum is taken over all \(n\geq 1\) and all independent random variables \(X_ 1,X_ 2,...,X_ n\) such that E \(X_ i=0\), \(1\leq i\leq n\), \(E X^ 2_ 1+...+E X^ 2_ n=B,\) and \(E X_ 1^{2m}+...+E X_ n^{2m}=A;\phi =(A/B)^{1/(2m-2)}\), and the random variable \(\eta_{\lambda}\) has Poisson distribution with \(\lambda =(B^ m/A)^{1/(m-1)}\).
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 4209195
zbMATH Keywords: sums of independent random variables
zbMATH Keywords: Poisson distribution
reviewed by: Zdzisław Rychlik
MaRDI profile type: Publication
cites work: Q3702198
cites work: On a Method of Calculation of Semi-Invariants
cites work: Q5512461
description: scientific article; zbMATH DE number 4209195