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On regular variation for infinitely divisible random vectors and additive processes
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2006 (English)In: Advances in Applied Probability, ISSN 0001-8678, E-ISSN 1475-6064, Vol. 38, no 1, 134-148 p.Article in journal (Refereed) Published
Abstract [en]

We study the tail behavior of regularly varying infinitely divisible random vectors and additive processes, i.e. stochastic processes with independent but not necessarily stationary increments. We show that the distribution of an infinitely divisible random vector is tail equivalent to its Levy measure and we study the asymptotic decay of the probability for an additive process to hit sets far away from the origin. The results are extensions of known univariate results to the multivariate setting; we exemplify some of the difficulties that arise in the multivariate case.

Place, publisher, year, edition, pages
2006. Vol. 38, no 1, 134-148 p.
Keyword [en]
multivariate regular variation, infinitely divisible distribution, additive process, Levy process, multivariate, convergence
National Category
Probability Theory and Statistics
URN: urn:nbn:se:kth:diva-15595DOI: 10.1239/aap/1143936144ISI: 000236720200008ScopusID: 2-s2.0-33646099385OAI: diva2:333637
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2012-03-07Bibliographically approved

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Hult, HenrikLindskog, Filip
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