Asymptotic Estimate of Number of Level Crossings of a Random Algebraic Polynomial

Abstract

We consider a polynomial equation where the number of level crossings can be found with dependent coefficients. The number of zeros and the upper bound for the above random algebraic polynomial with real coefficients is obtained. It is supposed that the coefficients are in dependent random variables identically distributed with expectation value zero and the variance and the third absolute moment being finite and non-zero and we must find the number of level crossings of the random algebraic polynomial with real coefficients which more approximate than other.