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- W1996215068 abstract "Let $X(t)$ be a stationary Gaussian process with continuous sample paths. The behavior of $|X(t)|$ as $t rightarrow infty$ is considered. In particular, conditions on the spectrum of the process are given which determine whether $lim sup_{trightarrowinfty}|X(t)|/(log t)^{frac{1}{2}} = operatorname{Const.} > 0$. These conditions are complete except when the spectrum of the process is continuous-singular. The main concern of this paper is to study the asymptotic behavior of some specific examples of $X(t)$ with continuous-singular spectra. Many examples are given showing the asymptotic behavior of stationary Gaussian processes with discrete spectra and their indefinite integrals." @default.
- W1996215068 created "2016-06-24" @default.
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- W1996215068 date "1974-08-01" @default.
- W1996215068 modified "2023-09-26" @default.
- W1996215068 title "Asymptotic Maxima of Continuous Gaussian Processes" @default.
- W1996215068 doi "https://doi.org/10.1214/aop/1176996613" @default.
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