A large deviation principle for Minkowski sums of heavy-tailed random compact convex sets with finite expectation
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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.
Originalsprog | Engelsk |
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Tidsskrift | Journal of Applied Probability |
Vol/bind | 48A |
Sider (fra-til) | 133-144 |
ISSN | 0021-9002 |
Status | Udgivet - 2011 |
Bibliografisk note
Special issue.
New Frontiers in Applied Probability : A Festschrift for Søren Asmussen. (Ed. by P. Glynn, T. Mikosch and T. Rolski)
ID: 36006460