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Number of real roots of a random trigonometric polynomial

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  • K. Farahmand

Abstract

We study the expected number of real roots of the random equation g 1 cos θ + g 2 cos 2 θ + … + g n cos n θ = K where the coefficients g j 's are normally distributed, but not necessarily all identical. It is shown that although this expected number is independent of the means of g j , ( j = 1 , 2 , … , n ) , it will depend on their variances. The previous works in this direction considered the identical distribution for the coefficients.

Suggested Citation

  • K. Farahmand, 1992. "Number of real roots of a random trigonometric polynomial," International Journal of Stochastic Analysis, Hindawi, vol. 5, pages 1-7, January.
    • Handle: RePEc:hin:jnijsa:241521
    DOI: 10.1155/S104895339200025X
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