A large deviation principle for Minkowski sums of heavy-tailed random compact convex sets with finite expectation
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We prove large deviation results for Minkowski sums Sn of independent and identically distributed 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, Pawlas and Samorodnitsky (2011) for generally nonconvex sets, where we assumed that the normalization of Sn grows faster than n.
Original language | English |
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Journal | Journal of Applied Probability |
Volume | 48A |
Pages (from-to) | 133-144 |
ISSN | 0021-9002 |
Publication status | Published - 2011 |
ID: 36006460