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

K. Farahmand

International Journal of Stochastic Analysis, 1997, vol. 10, 1-10

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.

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:740848

DOI: 10.1155/S1048953397000051

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