Large deviations for heavy-tailed random elements in convex cones

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:411

Article

Kopp, Christoph¹  Molchanov, Ilya¹ 

[1] Univ Bern, Inst Math Stat & Actuarial Sci, CH-3012 Bern, Switzerland

关键词: Large deviation;    Convex cone;    Heavy-tailed distribution;    Embedding;    Random set;   

DOI  :  10.1016/j.jmaa.2013.09.042

来源: Elsevier

【 摘 要 】

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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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