On the variance of the number of real zeros of a random trigonometric polynomial. (1997)

• Record Type: Journal Article
• Authors: Farahmand, K.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 10:Number 1(1997)
• Page Start: 57
• Page End: 66
• Publication Date: 1997
• Subjects: Gaussian random processes -- number of real roots -- number of crossings -- random trigonometric polynomial; 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/S1048953397000051
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : The asymptotic estimate of the expected number of real zeros of the polynomial T ( θ ) = g 1 cos θ + g 2 cos 2 θ + … + g n cos n θ where g j ( j = 1, 2, …, n ) is a sequence of independent normally distributed random variables is known. The present paper provides an upper estimate for the variance of such a number. To achieve this result we first present a general formula for the covariance of the number of real zeros of any normal process, ξ ( t ), occurring in any two disjoint intervals. A formula for the variance of the number of real zeros of ξ ( t ) follows from this result.