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The growth of the expected number of real zeros of a random polynomial

Part of: Stochastic analysis Stochastic processes

Published online by Cambridge University Press:  09 April 2009

Richard Glendinning
Richard Glendinning
Affiliation:
Department of Civil EngineeringUniversity of Newcastle upon TyneNewcastle upon Tyne NE1 7RU, England
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Abstract

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Let X0, X1…Xn,… be a stationary Gaussian process. We give sufficient conditions for the expected number of real zeros of the polynomial Qn (z) = Σnj =o X jzj to be (2/ π)log n as n tends to infinity.

Keywords

real zerosrandom polynomialsasymptotic growthstationary Gaussian processspectral densityuniformly mixingKac- Rice formulaToeplitz forms.

MSC classification

Secondary: 60H25: Random operators and equations 60G17: Sample path properties
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 1 , February 1989 , pp. 100 - 121
Copyright
Copyright © Australian Mathematical Society 1989

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