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Poisson approximation using the Stein-Chen method and coupling: Number of exceedances of Gaussian random variables. (English) Zbl 0713.60047

The title describes pretty much the content. For a family of dependent Gaussian random variables count the number of exceedances of a certain level. Approximate this distribution by a Poisson distribution. Here upper bounds for the total variation norm are given. The main mathematical tools are the Stein-Chen method and a coupling.
Reviewer: U.Rösler

MSC:

60G15 Gaussian processes
60F05 Central limit and other weak theorems
60G10 Stationary stochastic processes
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