A large deviation principle for Minkowski sums of heavy-tailed random compact convex sets with finite expectation
Research output: Contribution to journal › Journal article › Research › peer-review
Standard
A large deviation principle for Minkowski sums of heavy-tailed random compact convex sets with finite expectation. / Mikosch, Thomas Valentin; Pawlas, Zbynek; Samorodnitsky, Gennady .
In: Journal of Applied Probability, Vol. 48A, 2011, p. 133-144.Research output: Contribution to journal › Journal article › Research › peer-review
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - A large deviation principle for Minkowski sums of heavy-tailed random compact convex sets with finite expectation
AU - Mikosch, Thomas Valentin
AU - Pawlas, Zbynek
AU - Samorodnitsky, Gennady
N1 - Special issue. New Frontiers in Applied Probability : A Festschrift for Søren Asmussen. (Ed. by P. Glynn, T. Mikosch and T. Rolski)
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
M3 - Journal article
VL - 48A
SP - 133
EP - 144
JO - Journal of Applied Probability
JF - Journal of Applied Probability
SN - 0021-9002
ER -
ID: 36006460