## Journal of Applied Probability

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

#### Abstract

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.

#### Article information

Source
J. Appl. Probab., Volume 48A (2011), 133-144.

Dates
First available in Project Euclid: 18 October 2011

https://projecteuclid.org/euclid.jap/1318940461

Digital Object Identifier
doi:10.1239/jap/1318940461

Mathematical Reviews number (MathSciNet)
MR2865622

Zentralblatt MATH identifier
1235.60012

Subjects
Primary: 60F10: Large deviations
Secondary: 52A22: Random convex sets and integral geometry [See also 53C65, 60D05]

#### Citation

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