A large deviation principle for Minkowski sums of heavy-tailed random compact convex sets with finite expectation
Mikosch, Thomas; Pawlas, Zbynek; Samorodnitsky, Gennady
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.
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. }
random set; large deviations; regular variation; Minkowski sum