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Exceedence Measure of Classes of Algebraic Polynomials

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  • K. Farahmand

    (University of Ulster)

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.

Suggested Citation

  • K. Farahmand, 2003. "Exceedence Measure of Classes of Algebraic Polynomials," Journal of Theoretical Probability, Springer, vol. 16(2), pages 419-426, April.
    • Handle: RePEc:spr:jotpro:v:16:y:2003:i:2:d:10.1023_a:1023526828571
    DOI: 10.1023/A:1023526828571
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    References listed on IDEAS

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    1. Ramponi, A., 1999. "A note on the complex roots of complex random polynomials," Statistics & Probability Letters, Elsevier, vol. 44(2), pages 181-187, August.
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    1. Farahmand, K. & Stretch, C.T., 2008. "Algebraic polynomials with random non-symmetric coefficients," Statistics & Probability Letters, Elsevier, vol. 78(11), pages 1305-1313, August.

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