Abstract
The asymptotic estimate of the expected number of real zeros of the polynomial T(θ)=g1cosθ+g2cos2θ+…+gncosnθ where gj(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.