Let $\xi_0, \xi_1, \cdots, \xi_n, \cdots$ be a Gaussian stationary sequence of random variables. We study the asymptotic behavior of the mean number of real roots of the polynomial $P_n(x) = \xi_0 + \xi_1x + \cdots + \xi_nx^n$ as $n \rightarrow \infty$.
Publié le : 1981-06-14
Classification:
60-02,
Gaussian stationary sequence,
random polynomials,
real roots,
asymptotic behavior,
correlation function,
60G15
@article{1176994424,
author = {Shenker, M.},
title = {The Mean Number of Real Roots for One Class of Random Polynomials},
journal = {Ann. Probab.},
volume = {9},
number = {6},
year = {1981},
pages = { 510-512},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994424}
}
Shenker, M. The Mean Number of Real Roots for One Class of Random Polynomials. Ann. Probab., Tome 9 (1981) no. 6, pp. 510-512. http://gdmltest.u-ga.fr/item/1176994424/