Holst, Lars; Janson, Svante Poisson approximation using the Stein-Chen method and coupling: Number of exceedances of Gaussian random variables. (English) Zbl 0713.60047 Ann. Probab. 18, No. 2, 713-723 (1990). 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 Cited in 7 Documents MSC: 60G15 Gaussian processes 60F05 Central limit and other weak theorems 60G10 Stationary stochastic processes Keywords:number of exceedences; Poisson distribution; Stein-Chen method; coupling PDFBibTeX XMLCite \textit{L. Holst} and \textit{S. Janson}, Ann. Probab. 18, No. 2, 713--723 (1990; Zbl 0713.60047) Full Text: DOI