A large deviation principle for Minkowski sums of heavy-tailed random compact convex sets with finite expectation
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Abstract
We prove large deviation results for Minkowski sums of iid random
compact sets where we assume
that the summands have a regularly varying distribution and
finite expectation. The main focus is on random convex compact sets. The
results confirm the heavy-tailed large deviation heuristics:
large'' values of the sum are essentially due to the
largest''
summand. These results extend those in Mikosch et al. (2011) for generally
non-convex sets, where we assumed that the normalization of the sum
grows faster than the number of terms.
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Sponsorship
Thomas Mikosch's research is partly supported by
the Danish Natural Science Research Council (FNU) Grant
09-072331, ``Point process modelling and statistical inference''.
Zbyn\v ek Pawlas is partly supported by the Czech Ministry of Education,
research project MSM 0021620839 and by the Grant Agency of the Czech Republic,
grant P201/10/0472. Gennady Samorodnitsky's research is partially
supported by a US Army Research Office (ARO) grant W911NF-10-1-0289
and a National Science Foundation (NSF) grant DMS-1005903 at Cornell
University. }
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2010-08-16T13:27:58Z
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Keywords
random set; large deviations; regular variation; Minkowski sum
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technical report