Journal of Applied Mathematics and Stochastic Analysis
Volume 2008 (2008), Article ID 189675, 8 pages
On Different Classes of Algebraic Polynomials with Random Coefficients
Department of Mathematics, University of Ulster, Jordanstown, County Antrim BT37 0QB, Northern Ireland, UK
Received 27 February 2008; Accepted 20 April 2008
Academic Editor: Lev Abolnikov
Copyright © 2008 K. Farahmand et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The expected number of real zeros of the polynomial of the form , where is a sequence of standard Gaussian random variables, is known. For large it is shown that this expected number in is asymptotic to . In this paper, we show that this asymptotic value increases significantly to when we consider a polynomial in the form instead. We give the motivation for our choice of polynomial and also obtain some other characteristics for the polynomial, such as the expected number of level crossings or maxima. We note, and present, a small modification to the definition of our polynomial which improves our result from the above asymptotic relation to the equality.