The cluster index of regularly varying sequences with applications to limit theory for functions of multivariate Markov chains

• 成果类型: Article
• 署名作者: Mikosch, Thomas; Wintenberger, Olivier
• 署名单位: University of Copenhagen; Universite PSL; Universite Paris-Dauphine
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0504-1
• 发表日期: 2014
• 页码: 157-196
• 关键词: large deviations; sample autocorrelations; minimal conditions; extremal behavior; cramers condition; account

摘要

We introduce the cluster index of a multivariate stationary sequence and characterize the index in terms of the spectral tail process. This index plays a major role in limit theory for partial sums of sequences. We illustrate the use of the cluster index by characterizing infinite variance stable limit distributions and precise large deviation results for sums of multivariate functions acting on a stationary Markov chain under a drift condition.