EXCEEDANCE MEASURE OF RANDOM POLYNOMIALS

The present paper provides an asymptotic estimate for the mathematical expectation of the area cut off above a level K by a curve representi ng an algebraic or a trigonometric polynomial with independent random coefficients. The general idea of exceedance measure of a non-stationa ry stochastic process is adapted and modified to lead to the result. T here are many known asymptotic estimates for the expected number of cr ossings of such polynomials and the level K: It is shown that the cons tant K square K-n can exceed previously known values without affecting the behaviour or the polynomials.