J Austral Math Soc Ser A 46 pp100--121, 1989.

The Growth of the Expected Number of Real Zeros of a Random Polynomial

Richard Glendinning

(Received 27 January 1987; revised 8 July 1987)

Abstract

Let X₀, X₁, ..., X_n, ... be a stationary Gaussian process. We give sufficient conditions for the expected number of real zeros of the polynomial Q_n(z) = åⁿ_j=0X_jz^j to be (2/p)log n as n tends to infinity.

1980 AMS Subject Classification (1985 Revision): primary 60H25; secondary 60G17

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Authors

Richard Glendinning: Department of Civil Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU, England.

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