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On the average number of real zeros of a random trigonometric polynomial with dependent coefficients. II. (English) Zbl 0553.60063
[Part I has been submitted for publication in J. Indian Math. Soc.]
For the random trigonometric polynomial \(T(\theta)=\sum^{n}_{k=1}a_ k\cos k\theta\) (\(0\leq \theta \leq 2\pi)\) where \(a_ k\)’s are dependent normal random variables with mean zero, variance one and the correlation coefficient between any two random variables \((a_ i,a_ j)\) is \(p^{| i-j|}\), \(i\neq j\), the average number of real zeros is asymptotic to \(2n/\sqrt{3}\) for large \(n\).

MSC:
60H99 Stochastic analysis
60F15 Strong limit theorems
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