Large level crossings of a random polynomial

Large level crossings of a random polynomial

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Article ID: iaor1990664
Country: United States
Volume: 1
Start Page Number: 1
End Page Number: 7
Publication Date: Feb 1988
Journal: Journal of Applied Mathematics and Stochastic Analysis
Authors:
Abstract:

We know the expected number of times that a polynomial of degree n with independent random real coefficients asymptotically crosses the level K, when K is any real value such that (K2/n)⇒0 as n⇒•. The present paper shows that, when K is allowed to be large, this expected number of crossings reduces to only one. The coefficients of the polynomial are assumed to be normally distributed. It is shown that it is sufficient to let K≥exp(nf) where f is any function of n such that f⇒• as n⇒•.

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