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

Part of: Stochastic processes Stochastic analysis

Published online by Cambridge University Press:  09 April 2009

K. Farahmand  and
A. Grigorash
A. Grigorash
Affiliation:
Department of Mathematics, University of Ulster at Jordanstown, Co. Antrim, BT37 0QB, United Kingdom e-mail: K.Farahmand@ulst.ac.uk, AV.Grigorash@ulst.ac.uk
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Abstract

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An asymptotic estimate is derived for the expected number of extrema of a polynomial 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 asymptotic estimates for random polynomials with normal coefficients.

Keywords

number of real zerosreal rootsnumber of extremarandom algebraic polynomialsnormal stochastic processesasymptotic estimate.

MSC classification

Secondary: 60H99: None of the above, but in this section 60G15: Gaussian processes
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 70 , Issue 2 , April 2001 , pp. 225 - 234
Copyright
Copyright © Australian Mathematical Society 2001

References

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