HOMOGENEOUS MAPPINGS OF REGULARLY VARYING VECTORS

• 成果类型: Article
• 署名作者: Dyszewski, Piotr; Mikosch, Thomas
• 署名单位: University of Wroclaw; Technical University of Munich; University of Copenhagen
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1579
• 发表日期: 2020
• 页码: 2999-3026
• 关键词: INVERSE PROBLEMS

摘要

It is well known that the product of two independent regularly varying random variables with the same tail index is again regularly varying with this index. In this paper, we provide sharp sufficient conditions for the regular variation property of product-type functions of regularly varying random vectors, generalizing and extending the univariate theory in various directions. The main result is then applied to characterize the regular variation property of products of i.i.d. regularly varying quadratic random matrices and of solutions to affine stochastic recurrence equations under nonstandard conditions.