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Normal convergence of multidimensional shot noise and rates of this convergence

Published online by Cambridge University Press:  01 July 2016

Lothar Heinrich  and
Volker Schmidt
Lothar Heinrich
Affiliation:
Mining Academy of Freiberg
Volker Schmidt*
Affiliation:
Mining Academy of Freiberg
*
∗Postal address: Bergakademie Freiberg, Sektion Mathematik, DDR-9200 Freiberg, Bernhard-von-Cotta-Str. 2, GDR.
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Abstract

Using a representation formula expressing the mixed cumulants of realvalued random variables by corresponding moments, sufficient conditions are given for the normal convergence of suitably standardized shot noise assuming that the generating stationary point process is independently marked and Brillinger mixing and that its intensity tends to ∞. Furthermore, estimates for the rate of this normal convergence are obtained by exploiting a general lemma on probabilities of large deviations and on the rate of normal convergence.

Keywords

HIGH DENSITYCUMULANTSMARKED POINT PROCESSESMIXING CONDITION
Type
Research Article
Information
Advances in Applied Probability , Volume 17 , Issue 4 , December 1985 , pp. 709 - 730
Copyright
Copyright © Applied Probability Trust 1985 

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