Journal of Applied Probability
- J. Appl. Probab.
- Volume 48A (2011), 133-144.
A large deviation principle for Minkowski sums of heavy-tailed random compact convex sets with finite expectation
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.
J. Appl. Probab., Volume 48A (2011), 133-144.
First available in Project Euclid: 18 October 2011
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F10: Large deviations
Secondary: 52A22: Random convex sets and integral geometry [See also 53C65, 60D05]
Mikosch, Thomas; Pawlas, Zbyněk; Samorodnitsky, Gennady. A large deviation principle for Minkowski sums of heavy-tailed random compact convex sets with finite expectation. J. Appl. Probab. 48A (2011), 133--144. doi:10.1239/jap/1318940461. https://projecteuclid.org/euclid.jap/1318940461