LEVEL-CROSSINGS OF A RANDOM TRIGONOMETRIC POLYNOMIAL

This paper provides an asymptotic estimate for the expected number of K-level crossings of the random trigonometric polynomial g1 cos x + g2 cos 2x + ... + g(n) cos nx, where g(j) (j = 1, 2,... , n) are independent normally distributed random variables with mean mu and variance one. It is shown that the result for k = mu = 0 remains valid for any finite constant mu and any K such that (k2/n) --> 0 as n --> infinity.