Real zeros of random algebraic polynomials with binomial elements

A. Nezakati and K. Farahmand

International Journal of Stochastic Analysis, 2006, vol. 2006, 1-6

Abstract:

This paper provides an asymptotic estimate for the expected number of real zeros of a random algebraic polynomial a 0 + a 1 x + a 2 x 2 + … + a n − 1 x n − 1 . The coefficients a j ( j = 0 , 1 , 2 , … , n − 1 ) are assumed to be independent normal random variables with mean zero. For integers m and k = O ( log ⁡ n ) 2 the variances of the coefficients are assumed to have nonidentical value var ⁡ ( a j ) = ( k − 1 j − i k ) , where n = k ⋅ m and i = 0 , 1 , 2 , … , m − 1 . Previous results are mainly for identically distributed coefficients or when var ⁡ ( a j ) = ( n j ) . We show that the latter is a special case of our general theorem.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:013980

DOI: 10.1155/JAMSA/2006/13980

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