Mean number of real zeros of a random trigonometric polynomial IV. (1997)

• Record Type: Journal Article
• Authors: Wilkins, J. Ernest
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 10:Number 1(1997)
• Page Start: 67
• Page End: 70
• Publication Date: 1997
• Subjects: random polynomials -- real zeros; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953397000063
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : If a j ( j = 1, 2, …, n ) are independent, normally distributed random variables with mean 0 and variance 1, if p is one half of any odd positive integer except one, and if v n p is the mean number of zeros on ( 0, 2 π ) of the trigonometric polynomial a 1 cos x + 2 p a 2 cos 2 x + … + n p a n cos n x, then v n p = μ p { ( 2 n + 1 ) + D 1 p + ( 2 n + 1 ) − 1 D 2 p + ( 2 n + 1 ) − 2 D 3 p } + O { ( 2 n + 1 ) − 3 }, in which μ p = { ( 2 p + 1 ) / ( 2 p + 3 ) } ½, and D 1 p, D 2 p and D 3 p are explicitly stated constants.