Table of Contents
International Journal of Stochastic Analysis
Volume 2010, Article ID 931565, 10 pages
Research Article

Random Trigonometric Polynomials with Nonidentically Distributed Coefficients

Department of Mathematics, University of Ulster at Jordanstown, Co. Antrim, BT37 0QB, UK

Received 17 December 2009; Accepted 9 February 2010

Academic Editor: Bradford Allen

Copyright © 2010 K. Farahmand and T. Li. 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.


This paper provides asymptotic estimates for the expected number of real zeros of two different forms of random trigonometric polynomials, where the coefficients of polynomials are normally distributed random variables with different means and variances. For the polynomials in the form of π‘Ž 0 + π‘Ž 1 c o s πœƒ + π‘Ž 2 c o s 2 πœƒ + β‹― + π‘Ž 𝑛 c o s 𝑛 πœƒ and π‘Ž 0 + π‘Ž 1 c o s πœƒ + 𝑏 1 s i n πœƒ + π‘Ž 2 c o s 2 πœƒ + 𝑏 2 s i n 2 πœƒ + β‹― + π‘Ž 𝑛 c o s 𝑛 πœƒ + 𝑏 𝑛 s i n 𝑛 πœƒ , we give a closed form for the above expected value. With some mild assumptions on the coefficients we allow the means and variances of the coefficients to differ from each others. A case of reciprocal random polynomials for both above cases is studied.