The Annals of Probability

The Mean Number of Real Roots for One Class of Random Polynomials

M. Shenker

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Abstract

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 $n \rightarrow \infty$.

Article information

Source
Ann. Probab., Volume 9, Number 3 (1981), 510-512.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994424

Digital Object Identifier
doi:10.1214/aop/1176994424

Mathematical Reviews number (MathSciNet)
MR614636

Zentralblatt MATH identifier
0466.60041

JSTOR
links.jstor.org

Subjects
Primary: 60G15: Gaussian processes

Keywords
60-02 Gaussian stationary sequence random polynomials real roots asymptotic behavior correlation function

Citation

Shenker, M. The Mean Number of Real Roots for One Class of Random Polynomials. Ann. Probab. 9 (1981), no. 3, 510--512. doi:10.1214/aop/1176994424. https://projecteuclid.org/euclid.aop/1176994424


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