A large deviation principle for Minkowski sums of heavy-tailed random compact convex sets with finite expectation

Thomas Mikosch, Zbyněk Pawlas, Gennady Samorodnitsky
2011 Journal of Applied Probability  
We prove large deviation results for Minkowski sums S n 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
more » ... , where we assumed that the normalization of S n grows faster than n.
doi:10.1239/jap/1318940461 fatcat:f7cc5rtcbjdhbl6l35bc4a2fqq