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

Department of Mathematical Sciences

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.

Original language	English
Journal	Vestnik St Petersburg University - Mathematics
Volume	2011
Issue number	2
Pages (from-to)	70-78
ISSN	1063-4541
Publication status	Published - 2011

Access to Document

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

Cite this

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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.",

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AU - Samorodnitsky, Gennady

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PY - 2011

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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.

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VL - 2011

SP - 70

EP - 78

JO - Vestnik Sankt-Peterburgskogo Universiteta. Ser 1. Matematika Mekhanika Astronomiya

JF - Vestnik Sankt-Peterburgskogo Universiteta. Ser 1. Matematika Mekhanika Astronomiya

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