Process level moderate deviations for stabilizing functionals

Peter Eichelsbacher; Tomasz Schreiber

ESAIM: Probability and Statistics (2010)

  • Volume: 14, page 1-15
  • ISSN: 1292-8100

Abstract

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Functionals of spatial point process often satisfy a weak spatial dependence condition known as stabilization. In this paper we prove process level moderate deviation principles (MDP) for such functionals, which is a level-3 result for empirical point fields as well as a level-2 result for empirical point measures. The level-3 rate function coincides with the so-called specific information. We show that the general result can be applied to prove MDPs for various particular functionals, including random sequential packing, birth-growth models, germ-grain models and nearest neighbor graphs. 


How to cite

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Eichelsbacher, Peter, and Schreiber, Tomasz. "Process level moderate deviations for stabilizing functionals." ESAIM: Probability and Statistics 14 (2010): 1-15. <http://eudml.org/doc/250824>.

@article{Eichelsbacher2010,
abstract = {
Functionals of spatial point process often satisfy a weak spatial dependence condition known as stabilization. In this paper we prove process level moderate deviation principles (MDP) for such functionals, which is a level-3 result for empirical point fields as well as a level-2 result for empirical point measures. The level-3 rate function coincides with the so-called specific information. We show that the general result can be applied to prove MDPs for various particular functionals, including random sequential packing, birth-growth models, germ-grain models and nearest neighbor graphs. 
},
author = {Eichelsbacher, Peter, Schreiber, Tomasz},
journal = {ESAIM: Probability and Statistics},
keywords = {Moderate deviations; random Euclidean graphs; random sequential packing.; moderate deviation; random Euclidean graph; random sequential packing},
language = {eng},
month = {2},
pages = {1-15},
publisher = {EDP Sciences},
title = {Process level moderate deviations for stabilizing functionals},
url = {http://eudml.org/doc/250824},
volume = {14},
year = {2010},
}

TY - JOUR
AU - Eichelsbacher, Peter
AU - Schreiber, Tomasz
TI - Process level moderate deviations for stabilizing functionals
JO - ESAIM: Probability and Statistics
DA - 2010/2//
PB - EDP Sciences
VL - 14
SP - 1
EP - 15
AB - 
Functionals of spatial point process often satisfy a weak spatial dependence condition known as stabilization. In this paper we prove process level moderate deviation principles (MDP) for such functionals, which is a level-3 result for empirical point fields as well as a level-2 result for empirical point measures. The level-3 rate function coincides with the so-called specific information. We show that the general result can be applied to prove MDPs for various particular functionals, including random sequential packing, birth-growth models, germ-grain models and nearest neighbor graphs. 

LA - eng
KW - Moderate deviations; random Euclidean graphs; random sequential packing.; moderate deviation; random Euclidean graph; random sequential packing
UR - http://eudml.org/doc/250824
ER -

References

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