Average Number of Real Roots of Random Harmonic Equations

S. Bagh

Journal of Theoretical Probability, 1998, vol. 11, issue 4, 857-868

Abstract: Abstract Let {gk}be a sequence of normally distributed independent random variables with mathematical expectation zero and variance unity. Let ψ k (t ) (k = 0, 1, 2,...) be the normalized Jacobi polynomials orthogonal with respect to the interval [ − 1, 1 ]. Then it is proved that the average number of real roots of the random equations,Σ k=0 n gkψk(1)=C where Cis a constant, is asymptotically equal to n/√in the same interval when nis large and even for C → ∞ as long as C=O (n 2).

Keywords: Average number of real roots; Jacobi polynomial; Jensen's theorem (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1022616313073

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