Number of Level Crossings of a Random Trigonometric Polynomial

Abstract

The asymptotic estimates of the expected number of real zeros of the polynomial T( ) g1cos g2cos2 ......gncosn where gj (j=1, 2, n) is a sequence of independent normally distributed random variables is such a number. To achieve the result, we first present a general formula for the covariance of the number of real zeros of any normal process, e (t), occurring in any two disjoint intervals. A formula for the variance of
the number of real zeros of e (t) follows from this result.