Average Number of Real Zeros of Random Algebraic Polynomials Defined by the Increments of Fractional Brownian Motion

Safari Mukeru ()
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Safari Mukeru: University of South Africa

Journal of Theoretical Probability, 2019, vol. 32, issue 3, 1502-1524

Abstract: Abstract The study of random polynomials has a long and rich history. This paper studies random algebraic polynomials $$P_n(x) = a_0 + a_1 x + \cdots + a_{n-1} x^{n-1}$$ P n ( x ) = a 0 + a 1 x + ⋯ + a n - 1 x n - 1 where the coefficients $$(a_k)$$ ( a k ) are correlated random variables taken as the increments $$X(k+1) - X(k)$$ X ( k + 1 ) - X ( k ) , $$k\in \mathbb {N}$$ k ∈ N , of a fractional Brownian motion X of Hurst index $$0

Keywords: Random polynomials; Fractional Brownian motion; Real zeros; 26C10; 30B20; 60G22 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-018-0818-0

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