Functional large deviations for multivariate regularly varying random walks
Abstract
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 c\`{a}dl\`{a}g 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.
Cite
@article{arxiv.math/0602460,
title = {Functional large deviations for multivariate regularly varying random walks},
author = {Henrik Hult and Filip Lindskog and Thomas Mikosch and Gennady Samorodnitsky},
journal= {arXiv preprint arXiv:math/0602460},
year = {2007}
}
Comments
Published 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)