Exceedence Measure of Classes of Algebraic Polynomials

There is both mathematical and physical interest in the behaviour of the polynomial of the form . The coefficients a_j, j = 0,...,n are assumed to be independent normally distributed random variables with mean zero and variance ². In this paper by using the motion of exceedence measure for stochastic processes, for n large, we derive an asymptotic estimate for the expected area of the curve representing the above polynomial cut off by the x-axis. We show that our method can be used to obtain results for similar random polynomials.