Large deviations for heavy-tailed random elements in convex cones

Kopp, Christoph Peter; Molchanov, Ilya (2014). Large deviations for heavy-tailed random elements in convex cones. Journal of mathematical analysis and applications, 411(1), pp. 271-280. Elsevier 10.1016/j.jmaa.2013.09.042

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We prove large deviation results for sums of heavy-tailed random elements in rather general convex cones being semigroups equipped with a rescaling operation by positive real numbers. In difference to previous results for the cone of convex sets, our technique does not use the embedding of cones in linear spaces. Examples include the cone of convex sets with the Minkowski addition, positive half-line with maximum operation and the family of square integrable functions with arithmetic addition and argument rescaling.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Kopp, Christoph Peter and Molchanov, Ilya

Subjects:

500 Science > 510 Mathematics

ISSN:

0022-247X

Publisher:

Elsevier

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

01 Apr 2014 02:55

Last Modified:

08 Aug 2016 15:52

Publisher DOI:

10.1016/j.jmaa.2013.09.042

BORIS DOI:

10.7892/boris.41530

URI:

https://boris.unibe.ch/id/eprint/41530

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