On the rate of convergence of random polynomials of degree 3
type: Item
instance of: scholarly article
title: On the rate of convergence of random polynomials of degree 3
zbMATH Open document ID: 0998.60031
DOI: 10.1023/A:1011320010522
published in: Journal of Mathematical Sciences (New York)
publication date: 2002-06-16T00:00:00Z
review text: Let \(x_1,x_2,\dots,x_n\) be iid random variables. Let \(P_3=P_3(x_1,\dots,x_n)\) denote a sequence of homogeneous symmetric random polynomials of degree three and \(Z_3(x)=n^{-3/2}P_3(x)\). Let \(z=a_1N^3+a_2N\), where \(N\) is the standard normal law. The author obtains an estimate of the order of convergence rate as \(n^{-1/2}\) in the Lévy metric. It is really an improved estimate.
Mathematics Subject Classification ID: 60F99
zbMATH DE Number: 1756334
zbMATH Keywords: random polynomials
zbMATH Keywords: Lévy metric
zbMATH Keywords: rate of convergence
author: O. L. Yanushkyavichene
reviewed by: V. Thangaraj
MaRDI profile type: Publication
full work available at URL: a:1011320010522
OpenAlex ID: W127969941
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description: scientific article; zbMATH DE number 1756334