Geodesic
Rare events and Poisson point processes
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 26, Tome 466 (2017), pp. 109-119

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The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent terms by the accompanying compound Poisson laws may be interpreted as substantial quantitative estimates for the closeness between the sample containing independent observations of rare events and the Poisson point process which is obtained after a Poissonization of the initial sample. 
@article{ZNSL_2017_466_a7,
     author = {F. G\"otze and A. Yu. Zaitsev},
     title = {Rare events and {Poisson} point processes},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {109--119},
     publisher = {mathdoc},
     volume = {466},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_466_a7/}
}
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F. Götze; A. Yu. Zaitsev. Rare events and Poisson point processes. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 26, Tome 466 (2017), pp. 109-119. http://geodesic.mathdoc.fr/item/ZNSL_2017_466_a7/