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Functional large deviations for multivariate regularly varying random walks
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2005 (English)In: The Annals of Applied Probability, ISSN 1050-5164, Vol. 15, no 4, 2651-2680 p.Article in journal (Refereed) Published
Abstract [en]

We 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 cAdlAg 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 se-ments. 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.

Place, publisher, year, edition, pages
2005. Vol. 15, no 4, 2651-2680 p.
Keyword [en]
large deviations, regular variation, functional limit theorems, random, walks, long strange segments, convergence
URN: urn:nbn:se:kth:diva-15269DOI: 10.1214/105051605000000502ISI: 000234187900013ScopusID: 2-s2.0-30844459420OAI: diva2:333310
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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