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- W1990529283 abstract "Let ${xi(t)}_{t geq 0}$ be a stationary stochastic process, with one-dimensional distribution function $G$. We develop a method to determine an asymptotic expression for $Pr{sup_{0 leq t leq h} xi(t) > u}$, when $u uparrow sup{v: G(v) < 1}$, applicable when $G$ belongs to a domain of attraction of extremes, and we show that if $G$ belongs to such a domain, then so does the distribution function of $sup_{0 leq t leq h} xi(t)$. Applications are given to hitting probabilities for small sets for $mathbb{R}^m$-valued Gaussian processes and to extrema of Rayleigh processes. Further, we prove the Gumbel, Frechet and Weibull laws, for maxima over increasing intervals, when $G$ is type I-, type II- and type III-attracted, respectively, and we establish the asymptotic Poisson character of $varepsilon$-upcrossings and local $varepsilon$-maxima." @default.
- W1990529283 created "2016-06-24" @default.
- W1990529283 creator A5001593067 @default.
- W1990529283 date "1990-01-01" @default.
- W1990529283 modified "2023-10-12" @default.
- W1990529283 title "On Extremal Theory for Stationary Processes" @default.
- W1990529283 doi "https://doi.org/10.1214/aop/1176990940" @default.
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