On the Expected Number of Level Crossings of Random Trigonometric Polynomials.

This paper provides an asymptotic estimate for the expected number of level-crossings of random trigonometric polynomials a 0 (ω) + a 1 (ω)cosΘ + ··· + a n (ω)cos n Θ, where a j (ω), j = 0,..., n are k groups of independent normally distributed random variables with means μ i and variances , i = 1,..., k . It is shown that in order to obtain our result we need charac-teristics, namely μ i and , i = 1,..., k , to be any bounded absolute constants. [ABSTRACT FROM AUTHOR]