Tid: 13 december 2004 kl 1515-1700

Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!

Föredragshållare: Filip Lindskog, Matematisk statistik, KTH

Titel: Functional large deviations for multivariate regularly varying random walks

Sammanfattning: We extend classical results by A.V. Nagaev (1969) on large deviations for sums of iid regularly varying random variables to partial sum processes of iid 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 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.

Joint work with Henrik Hult, Thomas Mikosch and Gennady Samorodnitsky.

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