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The Danish National Research Foundation:
Network in Mathematical Physics and Stochastics

Funded by The Danish National Research Foundation

MPS-RR 2004-27
November 2004

Functional large deviations for multivariate regularly varying random walks

by: Henrik Hult , Filip Lindskog , Thomas Mikosch


We extend classical results by A.V. Nagaev (1969) on large deviations for sums of iid regularly varying random walks 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 càdàg 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.

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