On the equidistribution of polynomials of normal random variables
type: Item
instance of: scholarly article
title: On the equidistribution of polynomials of normal random variables
zbMATH Open document ID: 0836.60011
DOI: 10.1007/BF02335391
published in: Lithuanian Mathematical Journal
publication date: 1995-09-18T00:00:00Z
review text: Let \(N_1, \dots, N_l\) be random variables \(N(0,1)\) with correlation coefficients \(\rho_{ij}\). Let \(a_2, \dots, a_k\), \(b_1, \dots, b_l\), \(a_2', \dots, a_k'\), \(b_1', \dots, b_l'\) be some coefficients and \(X {\buildrel \text{d} \over =} Y\) denote the equidistribution of random variables \(X\) and \(Y\). A necessary and sufficient condition for \[ a_k N^k_1 + \cdots + a_2 N^2_1 + b_1 N_1 + \cdots + b_l N_l {\buildrel \text{d} \over =} a_k' N_1^k + \cdots + a_2' N_1^2 + b_1' N_1 + \cdots + b_l' N_l \] is proved by using properties of coefficients and of the \(\rho_{ij}\). This theorem is important for the study of the convergence (of the limit behaviour) of certain normed random polynomials.
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 794512
zbMATH Keywords: polynomials of random variables
zbMATH Keywords: equidistribution of random variables
zbMATH Keywords: random polynomials
author: O. L. Yanushkyavichene
reviewed by: Pavel Froněk
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf02335391
OpenAlex ID: W2075189939
description: scientific article; zbMATH DE number 794512