On the number of real zeros of a random trigonometric polynomial
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- by M. Sambandham PDF
- Trans. Amer. Math. Soc. 238 (1978), 57-70 Request permission
Abstract:
For the random trigonometric polynomial \[ \sum \limits _{n = 1}^N {{g_n}(t)\cos n\theta ,} \] where ${g_n}(t),0 \leqslant t \leqslant 1$, are dependent normal random variables with mean zero, variance one and joint density function \[ |M{|^{1/2}}{(2\pi )^{ - N/2}}\exp [ - (1/2)\bar a’M\bar a]\] where ${M^{ - 1}}$ is the moment matrix with ${\rho _{ij}} = \rho ,0 < \rho < 1,i \ne j,i,j = 1,2, \ldots ,N$ and $\bar a$ is the column vector, we estimate the probable number of zeros.References
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Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 238 (1978), 57-70
- MSC: Primary 60G17
- DOI: https://doi.org/10.1090/S0002-9947-1978-0461648-4
- MathSciNet review: 0461648