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

Thomas Valentin Mikosch; Olivier Wintenberger

doi:10.1007/s00440-013-0504-1

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

Thomas Valentin Mikosch, Olivier Wintenberger

Department of Mathematical Sciences

14 Citations (Scopus)

Abstract

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.

Original language	English
Journal	Probability Theory and Related Fields
Volume	159
Pages (from-to)	157-196
ISSN	0178-8051
DOIs	https://doi.org/10.1007/s00440-013-0504-1
Publication status	Published - Jun 2014

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abstract = "We introduce the cluster index of a multivariate stationary sequence andcharacterize the index in terms of the spectral tail process. This index plays a majorrole in limit theory for partial sums of sequences. We illustrate the use of the clusterindex by characterizing infinite variance stable limit distributions and precise largedeviation results for sums of multivariate functions acting on a stationary Markovchain under a drift condition.",

author = "Mikosch, {Thomas Valentin} and Olivier Wintenberger",

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AU - Mikosch, Thomas Valentin

AU - Wintenberger, Olivier

PY - 2014/6

Y1 - 2014/6

N2 - We introduce the cluster index of a multivariate stationary sequence andcharacterize the index in terms of the spectral tail process. This index plays a majorrole in limit theory for partial sums of sequences. We illustrate the use of the clusterindex by characterizing infinite variance stable limit distributions and precise largedeviation results for sums of multivariate functions acting on a stationary Markovchain under a drift condition.

AB - We introduce the cluster index of a multivariate stationary sequence andcharacterize the index in terms of the spectral tail process. This index plays a majorrole in limit theory for partial sums of sequences. We illustrate the use of the clusterindex by characterizing infinite variance stable limit distributions and precise largedeviation results for sums of multivariate functions acting on a stationary Markovchain under a drift condition.

U2 - 10.1007/s00440-013-0504-1

DO - 10.1007/s00440-013-0504-1

M3 - Journal article

SN - 0178-8051

VL - 159

SP - 157

EP - 196

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

ER -

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

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