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Teor. Veroyatnost. i Primenen., 1983, Volume 28, Issue 4, Pages 668–678 (Mi tvp2215)  

Asymptotic properties of the point processes of rare events in Gaussian fields. I

U. Zähle

GDR

Abstract: The asymptotic behaviour of point processes, generated by arbitrary rare events defined on the stationary discrete Gaussian vector fields, is studied. This paper contains some sufficient conditions for the weak convergence (after a suitable change of a parameter space) of the rare events point processes to a Poisson process. These conditions are weaker than well-known conditions for the special case of high level crossings.

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English version:
Theory of Probability and its Applications, 1984, 28:4, 703–713

Bibliographic databases:

Received: 12.05.1980

Citation: U. Zähle, “Asymptotic properties of the point processes of rare events in Gaussian fields. I”, Teor. Veroyatnost. i Primenen., 28:4 (1983), 668–678; Theory Probab. Appl., 28:4 (1984), 703–713

Citation in format AMSBIB
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\by U.~Z\"ahle
\paper Asymptotic properties of the point processes of rare events in Gaussian fields.~I
\jour Teor. Veroyatnost. i Primenen.
\yr 1983
\vol 28
\issue 4
\pages 668--678
\mathnet{http://mi.mathnet.ru/tvp2215}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=726893}
\zmath{https://zbmath.org/?q=an:0527.60034}
\transl
\jour Theory Probab. Appl.
\yr 1984
\vol 28
\issue 4
\pages 703--713
\crossref{https://doi.org/10.1137/1128069}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984TV66700005}


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