The cluster index of regularly varying sequences with applications to limit theory for functions of multivariate Markov chains
Wintenberger, Olivier; Mikosch, Thomas (2014), The cluster index of regularly varying sequences with applications to limit theory for functions of multivariate Markov chains, Probability Theory and Related Fields, 159, 1-2, p. 157-196. http://dx.doi.org/10.1007/s00440-013-0504-1
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00806306
Journal nameProbability Theory and Related Fields
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Abstract (EN)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.
Subjects / KeywordsGARCH; large deviation principle; central limit theorem; regular variation; Markov processes
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