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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.
@article{PS_2010__14__1_0,
author = {Eichelsbacher, Peter and Schreiber, Tomasz},
title = {Process level moderate deviations for stabilizing functionals},
journal = {ESAIM: Probability and Statistics},
pages = {1--15},
publisher = {EDP-Sciences},
volume = {14},
year = {2010},
doi = {10.1051/ps:2008027},
mrnumber = {2640365},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2008027/}
}
TY - JOUR AU - Eichelsbacher, Peter AU - Schreiber, Tomasz TI - Process level moderate deviations for stabilizing functionals JO - ESAIM: Probability and Statistics PY - 2010 SP - 1 EP - 15 VL - 14 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ps:2008027/ DO - 10.1051/ps:2008027 LA - en ID - PS_2010__14__1_0 ER -
%0 Journal Article %A Eichelsbacher, Peter %A Schreiber, Tomasz %T Process level moderate deviations for stabilizing functionals %J ESAIM: Probability and Statistics %D 2010 %P 1-15 %V 14 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ps:2008027/ %R 10.1051/ps:2008027 %G en %F PS_2010__14__1_0
Eichelsbacher, Peter; Schreiber, Tomasz. Process level moderate deviations for stabilizing functionals. ESAIM: Probability and Statistics, Tome 14 (2010), pp. 1-15. doi: 10.1051/ps:2008027
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