International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 1997 / Article

Open Access

Volume 10 |Article ID 296454 | 4 pages | https://doi.org/10.1155/S1048953397000063

Mean number of real zeros of a random trigonometric polynomial IV

Received01 Sep 1995
Revised01 May 1996

Abstract

If aj(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 vnp is the mean number of zeros on (0,2π) of the trigonometric polynomial a1cosx+2pa2cos2x++npancosnx, then vnp=μp{(2n+1)+D1p+(2n+1)1D2p+(2n+1)2D3p}+O{(2n+1)3}, in which μp={(2p+1)/(2p+3)}½, and D1p, D2p and D3p are explicitly stated constants.

Copyright © 1997 Hindawi Publishing Corporation. 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.

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