On the average number of real zeros of a random trigonometric polynomial with dependent coefficients. II
type: Item
instance of: scholarly article
title: On the average number of real zeros of a random trigonometric polynomial with dependent coefficients. II
zbMATH Open document ID: 0553.60063
author: N. G. Renganathan
author: M. Sambandham
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1984-01-01T00:00:00Z
review text: [Part I has been submitted for publication in J. Indian Math. Soc.] For the random trigonometric polynomial \(T(\theta)=\sum^{n}_{k=1}a_ k\cos k\theta\) (\(0\leq \theta \leq 2\pi)\) where \(a_ k\)'s are dependent normal random variables with mean zero, variance one and the correlation coefficient between any two random variables \((a_ i,a_ j)\) is \(p^{| i-j|}\), \(i\neq j\), the average number of real zeros is asymptotic to \(2n/\sqrt{3}\) for large \(n\).
Mathematics Subject Classification ID: 60H99
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 3881612
zbMATH Keywords: random trigonometric polynomial
zbMATH Keywords: average number of real zeros
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3881612