Large deviations for Minkowski sums of heavy-tailed generally non-convex random compact sets
Author
Mikosch, Thomas
Pawlas, Zbynek
Samorodnitsky, Gennady
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. The
result confirms the heavy-tailed large deviation heuristics:
large'' values of the sum are essentially due to the largest''
summand.
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.
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.
Date Issued
2010-08-16T14:36:00Z
Keywords
Type
technical report