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

Mikosch, TV, Pawlas, Z & Samorodnitsky, G 2011, 'A large deviation principle for Minkowski sums of heavy-tailed random compact convex sets with finite expectation', Journal of Applied Probability, vol. 48A, pp. 133-144. <http://projecteuclid.org/download/pdfview_1/euclid.jap/1318940461>

APA

Mikosch, T. V., Pawlas, Z., & Samorodnitsky, G. (2011). A large deviation principle for Minkowski sums of heavy-tailed random compact convex sets with finite expectation. Journal of Applied Probability, 48A, 133-144. http://projecteuclid.org/download/pdfview_1/euclid.jap/1318940461

Vancouver

Mikosch TV, Pawlas Z, Samorodnitsky G. A large deviation principle for Minkowski sums of heavy-tailed random compact convex sets with finite expectation. Journal of Applied Probability. 2011;48A:133-144.

Author

Mikosch, Thomas Valentin ; Pawlas, Zbynek ; Samorodnitsky, Gennady . / A large deviation principle for Minkowski sums of heavy-tailed random compact convex sets with finite expectation. In: Journal of Applied Probability. 2011 ; Vol. 48A. pp. 133-144.

Bibtex

@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",
language = "English",
volume = "48A",
pages = "133--144",
journal = "Journal of Applied Probability",
issn = "0021-9002",
publisher = "Applied Probability Trust",

}

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