Number of real roots of a random trigonometric polynomial

Number of real roots of a random trigonometric polynomial

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Article ID: iaor1997303
Country: United States
Volume: 5
Issue: 4
Start Page Number: 307
End Page Number: 314
Publication Date: Oct 1992
Journal: Journal of Applied Mathematics and Stochastic Analysis
Authors:
Keywords: mathematics
Abstract:

The paper studies the expected number of real roots of the random equation g1cosθ+g2cos2θ+...+gncosnθ=K where the coefficients gjs are normally distributed, but not necessarily all identical. It is shown that although this expected number is independent of the means of gj, j=1,2,...,n, it will depend on their variances. The previous works in this direction considered the identical distribution for the coefficients.

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