Exceedence Measure of Classes of Algebraic Polynomials

K. Farahmand ()
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K. Farahmand: University of Ulster

Journal of Theoretical Probability, 2003, vol. 16, issue 2, 419-426

Abstract: Abstract There is both mathematical and physical interest in the behaviour of the polynomial of the form $$a_0 + a_1 (_{\text{1}}^n {\kern 1pt} )^{1/2} x + a_2 (_{\text{2}}^n {\kern 1pt} )^{1/2} x^2 + \cdots + a_n (_n^n {\kern 1pt} )^{1/2} x^n $$ . The coefficients a j , j = 0,...,n are assumed to be independent normally distributed random variables with mean zero and variance σ 2. In this paper by using the motion of exceedence measure for stochastic processes, for n large, we derive an asymptotic estimate for the expected area of the curve representing the above polynomial cut off by the x-axis. We show that our method can be used to obtain results for similar random polynomials.

Keywords: exceedence measure; number of real zeros; random algebraic polynomials; Kac–Rice formula; random variables (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/A:1023526828571

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