A characterization of multivariate regular variation

• 成果类型: Article
• 署名作者: Basrak, B; Davis, RA; Mikosch, T
• 署名单位: Colorado State University System; Colorado State University Fort Collins; University of Copenhagen
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2002
• 页码: 908-920
• 关键词: sample autocorrelations; CONVERGENCE

摘要

We establish the equivalence between the multivariate regular variation of a random vector and the univariate regular variation of all linear combinations of the components of such a vector. According to a classical result of Kesten [Acta Math. 131 (1973) 207-248], this result implies that stationary solutions to multivariate linear stochastic recurrence equations are regularly varying. Since GARCH processes can be embedded in such recurrence equations their finite-dimensional distributions are regularly varying.