Funded by The Danish National Research Foundation

MPS-RR 2004-27

November 2004

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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