On the variance of the number of real zeros of a random trigonometric polynomial. (1997) - Farahmand, K.
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.