Functional large deviations for multivariate regularly varying random walks

Details Functional large deviations for multivariate regularly varying random walks Functional large deviations for multivariate regularly varying random walks

2006-02-21

arxiv.org/abs/math/0602460v1

Annals of Applied Probability 2005, Vol. 15, No. 4, 2651-2680

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051605000000502 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051605000000502

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.

Affiliated with

Also associated with

No associations

Rating

Functional large deviations for multivariate regularly varying random walks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Functional large deviations for multivariate regularly varying random walks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Functional large deviations for multivariate regularly varying random walks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-454471