The [formula omitted]-level crossings of a random algebraic polynomial with dependent coefficients

Abstract

For a random polynomial with standard normal coefficients, two cases of the K -level crossings have been considered by Farahmand. For independent coefficients, Farahmand derived an asymptotic value for the expected number of level crossings, even if K grows to infinity. Alternatively, he showed that coefficients with a constant covariance have half as many crossings. Given these results, the purpose of this paper is to study the behavior for dependent standard normal coefficients where the covariance is decaying. Using similar techniques to Farahmand, we will show that for a wide range of covariance functions behavior similar to the independent case can be expected.