Journal of Applied Mathematics and Stochastic Analysis
Volume 5 (1992), Issue 4, Pages 307-313
doi:10.1155/S104895339200025X
Number of real roots of a random trigonometric polynomial
University of Ulster, Department of Mathematics, Jordanstown, Co Antrim, BT37 0QB , United Kingdom
Received 1 December 1991; Revised 1 September 1992
Copyright © 1992 K. Farahmand. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We study the expected number of real roots of the random
equation g1cosθ+g2cos2θ+…+gncosnθ=K where the coefficients
gj's are normally distributed, but not necessarily all identical. It is
shown that although this expected number is independent of the means
of gj, (j=1,2,…,n), it will depend on their variances. The previous
works in this direction considered the identical distribution for the
coefficients.