Functional large deviations for multivariate regularly varying random walks

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dc.creatorHult, Henrik
dc.creatorLindskog, Filip
dc.creatorMikosch, Thomas
dc.creatorSamorodnitsky, Gennady
dc.date2006-02-21
dc.date.accessioned2026-07-07T07:03:38Z
dc.date.available2026-07-07T07:03:38Z
dc.descriptionWe extend classical results by A. V. Nagaev [Izv. Akad. Nauk UzSSR Ser. Fiz.--Mat. Nauk 6 (1969) 17--22, Theory Probab. Appl. 14 (1969) 51--64, 193--208] on large deviations for sums of i.i.d. regularly varying random variables to partial sum processes of i.i.d. regularly varying vectors. The results are stated in terms of a heavy-tailed large deviation principle on the space of càdlàg functions. We illustrate how these results can be applied to functionals of the partial sum process, including ruin probabilities for multivariate random walks and long strange segments. These results make precise the idea of heavy-tailed large deviation heuristics: in an asymptotic sense, only the largest step contributes to the extremal behavior of a multivariate random walk.
dc.descriptionPublished at http://dx.doi.org/10.1214/105051605000000502 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0602460
dc.identifierhttp://arxiv.org/abs/math/0602460
dc.identifierAnnals of Applied Probability 2005, Vol. 15, No. 4, 2651-2680
dc.identifierdoi:10.1214/105051605000000502
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/109051
dc.subjectProbability
dc.subject60F10, 60F17, 60G50, 60B12 (Primary)
dc.titleFunctional large deviations for multivariate regularly varying random walks
dc.typetext

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