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

Thomas Valentin Mikosch; Zbynek Pawlas; Gennady  Samorodnitsky

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

Thomas Valentin Mikosch, Zbynek Pawlas, Gennady Samorodnitsky

Department of Mathematical Sciences

2 Citations (Scopus)

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.

Original language	English
Journal	Journal of Applied Probability
Volume	48A
Pages (from-to)	133-144
ISSN	0021-9002
Publication status	Published - Aug 2011

Access to Document

http://projecteuclid.org/download/pdfview_1/euclid.jap/1318940461

Cite this

@article{50cf07c9e523414fa4820487e558aa6e,

title = "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. ",

author = "Mikosch, {Thomas Valentin} and Zbynek Pawlas and Gennady Samorodnitsky",

note = "Special issue. New Frontiers in Applied Probability : A Festschrift for S{\o}ren Asmussen. (Ed. by P. Glynn, T. Mikosch and T. Rolski)",

year = "2011",

month = aug,

language = "English",

volume = "48A",

pages = "133--144",

journal = "Journal of Applied Probability",

issn = "0021-9002",

publisher = "Applied Probability Trust",

}

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 - 2011/8

Y1 - 2011/8

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

SN - 0021-9002

VL - 48A

SP - 133

EP - 144

JO - Journal of Applied Probability

JF - Journal of Applied Probability

ER -