Extrema of random algebraic polynomials with non-identically distributed normal coefficients

Authors
Farahmand, K Grigorash, A
Citation
K. Farahmand et A. Grigorash, Extrema of random algebraic polynomials with non-identically distributed normal coefficients, J AUS MAT A, 70, 2001, pp. 225-233
Citations number
13
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS
ISSN journal
02636115 → ACNP
Volume
70
Year of publication
2001
Part
2
Pages
225 - 233
Database
ISI
SICI code
0263-6115(200104)70:<225:EORAPW>2.0.ZU;2-I
Abstract
An asymptotic estimate is derived for the expected number of extrema of a p olynomial a(0) + a(1)((n)(1))(1/2)x + a(2)((n)(2))(1/2)x(2) + ... + a(n)((n )(n))(1/2)x(n) whose independent normal coefficients possess non-equal non- zero mean values. A result is presented that generalizes in terms of normal processes the analytical device used for construction of similar asymptoti c estimates for random polynomials with normal coefficients.