Abstract:
This paper is devoted to limit theorems for the maxima of functions of dependent Gaussian time series. We investigate the asymptotic behavior of the normalized sequence of maxima in the case when the correlation function of the underlying process decays slower than logarithmically. Under certain natural assumptions on the transform, it is shown that no nontrivial limit distribution exists when the transform of a Gaussian random variable lies in the domain of attraction of the Frechet distribution. Moreover, a limit theorem is obtained for the case when the transform has a Weibull-like distribution.
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