LEVEL-CROSSINGS OF A RANDOM TRIGONOMETRIC POLYNOMIAL WITH DEPENDENT COEFFICIENTS

This paper provides an asymptotic estimate for the expected number of K-level crossings of the random trigonometric polynomial g(1) cos x g(2) cos 2x + ... + g(n) cos nx where g(j)(j = 1, 2,..., n) are depend ent normally distributed random variables with mean zero and variance one. The two cases of rho(jr), the correlation coeffiecient between th e j-th and r-th coefficients, being either (i) constant, or (ii) rho(\ j-r\) j not equal r, 0 < rho < 1, are considered. It is shown that the previous result for rho(jr) = 0 still remains valid for both cases.