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Process level moderate deviations for stabilizing functionals

Published online by Cambridge University Press:  07 October 2008

Peter Eichelsbacher  and
Tomasz Schreiber
Peter Eichelsbacher
Affiliation:
Fakultät für Mathematik, Ruhr-Universität Bochum, NA 3/68, 44780 Bochum, Germany; peter.eichelsbacher@ruhr-uni-bochum.de
Tomasz Schreiber
Affiliation:
Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Toruń, Poland; tomeks@mat.uni.torun.pl
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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. 


Keywords

Moderate deviationsrandom Euclidean graphsrandom sequential packing.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 14 , 2010 , pp. 1 - 15
Copyright
© EDP Sciences, SMAI, 2010

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