On regular variation for infinitely divisible random vectors and additive processes
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
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.
multivariate regular variation, infinitely divisible distribution, additive process, Levy process, multivariate, convergence
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:kth:diva-15595DOI: 10.1239/aap/1143936144ISI: 000236720200008ScopusID: 2-s2.0-33646099385OAI: oai:DiVA.org:kth-15595DiVA: diva2:333637
QC 201005252010-08-052010-08-052012-03-07Bibliographically approved