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On the variance of the number of real zeros of a random trigonometric polynomial

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  • K. Farahmand

Abstract

The asymptotic estimate of the expected number of real zeros of the polynomial T ( θ ) = g 1 cos θ + g 2 cos 2 θ + … + g n cos n θ where g j ( j = 1 , 2 , … , n ) is a sequence of independent normally distributed random variables is known. The present paper provides an upper estimate for the variance of such a number. To achieve this result we first present a general formula for the covariance of the number of real zeros of any normal process, ξ ( t ) , occurring in any two disjoint intervals. A formula for the variance of the number of real zeros of ξ ( t ) follows from this result.

Suggested Citation

  • K. Farahmand, 1997. "On the variance of the number of real zeros of a random trigonometric polynomial," International Journal of Stochastic Analysis, Hindawi, vol. 10, pages 1-10, January.
    • Handle: RePEc:hin:jnijsa:740848
    DOI: 10.1155/S1048953397000051
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