Volume 1, Issue 2

Measures of Maxima & Minima of a Cauchy Random Polynomial

Author

A. K. Mansingh1 , P.K.Mishra2 , B.Sahu3 , S.B.Sahu3

Abstract

Abstract:

The aim of this paper is to estimate the number of real zeros of a Cauchy random polynomial under different condition when the coefficients belong to the domain of attraction of Cauchy law. Let ∑= n r r G r WX 0 )( be a Cauchy random algebraic polynomial of degree n, whose coefficients Gr (X)’s identically distributed independent random variables belonging to the domain of attraction of Cauchy distribution. Then there exists a positive integer n0, such that for n>n0, the number of real roots of most of the equation ∑= n r r Gr WX 0 )( =0 is atmost µ (log n) 2 except for a set of measure atmost , n µ s1 0 ' − where µ and µ / are positive constants and 0

DOI

https://doi.org/10.62226/ijarst20120232

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