Large deviations for Minkowski sums of heavy-tailed generally non-convex random compact sets

Thomas Valentin Mikosch; Zbynek Pawlas; Gennady Samorodnitsky

Large deviations for Minkowski sums of heavy-tailed generally non-convex random compact sets

Thomas Valentin Mikosch, Zbynek Pawlas, Gennady Samorodnitsky

Institut for Matematiske Fag

Abstract

We prove large deviation results for Minkowski sums of iid random compact sets where
we assume that the summands have a regularly varying distribution. The result confirms
the heavy-tailed large deviation heuristics: “large” values of the sum are essentially due to
the “largest” summand.

Originalsprog	Engelsk
Tidsskrift	Vestnik St Petersburg University - Mathematics
Vol/bind	2011
Udgave nummer	2
Sider (fra-til)	70-78
ISSN	1063-4541
Status	Udgivet - 2011

Adgang til dokumentet

http://www.math.ku.dk/~mikosch/Preprint/Petrov/mikosch.pdf

Citationsformater

@article{8c9cda3fe9ac4ed7a984c543f9351d16,

title = "Large deviations for Minkowski sums of heavy-tailed generally non-convex random compact sets",

abstract = "We prove large deviation results for Minkowski sums of iid random compact sets wherewe assume that the summands have a regularly varying distribution. The result confirmsthe heavy-tailed large deviation heuristics: “large” values of the sum are essentially due tothe “largest” summand.",

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

note = "Special Issue in Honor of Valentin V. Petrov",

year = "2011",

language = "English",

volume = "2011",

pages = "70--78",

journal = "Vestnik St Petersburg University - Mathematics",

issn = "1063-4541",

publisher = "Allerton Press Inc.",

number = "2",

}

TY - JOUR

T1 - Large deviations for Minkowski sums of heavy-tailed generally non-convex random compact sets

AU - Mikosch, Thomas Valentin

AU - Pawlas, Zbynek

AU - Samorodnitsky, Gennady

N1 - Special Issue in Honor of Valentin V. Petrov

PY - 2011

Y1 - 2011

N2 - We prove large deviation results for Minkowski sums of iid random compact sets wherewe assume that the summands have a regularly varying distribution. The result confirmsthe heavy-tailed large deviation heuristics: “large” values of the sum are essentially due tothe “largest” summand.

AB - We prove large deviation results for Minkowski sums of iid random compact sets wherewe assume that the summands have a regularly varying distribution. The result confirmsthe heavy-tailed large deviation heuristics: “large” values of the sum are essentially due tothe “largest” summand.

M3 - Journal article

SN - 1063-4541

VL - 2011

SP - 70

EP - 78

JO - Vestnik St Petersburg University - Mathematics

JF - Vestnik St Petersburg University - Mathematics

IS - 2

ER -