The cluster index of regularly varying sequences with applications to limit theory for functions of multivariate Markov chains
type: Dataset
contact point: Organization
  fn: CCSD
keyword: regular-variation
keyword: journal-articles
keyword: ams-2000-subject-classifications-primary-60j05-secondary-60f10
keyword: statthstatistics-statstatistics-theory-statth
keyword: mathmath-stmathematics-mathstatistics-mathst
keyword: garch
keyword: ams-2000-subject-classifications-primary-60j05-secondary-60f10-60f05-60g70-markov-processes-regula
keyword: infoeu-reposemanticsarticle
keyword: mathmath-prmathematics-mathprobability-mathpr
keyword: large-deviation-principle
keyword: 60f05
keyword: markov-processes
keyword: 60g70-markov-processes
keyword: central-limit-theorem
keyword: primary-60j05-secondary-60f10-60f05-60g70
landing page: 0178-8051
description: We introduce the cluster index of a multivariate regularly varying 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 regularly varying 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.
issued: 2026-05-11T20:41:21.567079
language: en
modified: 2026-05-11T20:41:21.567085

test_moissonnage_selune
type: Agent

The cluster index of regularly varying sequences with applications to limit theory for functions of multivariate Markov chains
type: Distribution
access URL: https://hal.science/hal-00806306
format: HTML
issued: 2026-05-11T20:41:21.580520
modified: 2026-05-11T20:41:21.523430