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

被引：0
|
作者：
Thomas Mikosch
Olivier Wintenberger
机构：
[1] University of Copenhagen,Department of Mathematics
[2] Université de Paris-Dauphine,Centre De Recherche en Mathématiques de la Décision
[3] Place du Maréchal De Lattre De Tassigny,undefined
来源：
Probability Theory and Related Fields | 2014年 / 159卷
关键词：
Markov processes; Regular variation; Central limit theorem; Large deviation principle; GARCH; Primary 60J05; Secondary 60F10; 60F05; 60G70;
D O I：
暂无
中图分类号：
学科分类号：
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.
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页码：157 / 196
页数：39
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