English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

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 randomvariables to partial sum processes of i.i.d. regularly varying vectors. Theresults are stated in terms of a heavy-tailed large deviation principle on thespace of c\`{a}dl\`{a}g functions. We illustrate how these results can beapplied to functionals of the partial sum process, including ruin probabilitiesfor multivariate random walks and long strange segments. These results makeprecise the idea of heavy-tailed large deviation heuristics: in an asymptoticsense, only the largest step contributes to the extremal behavior of amultivariate random walk.

Functional large deviations for multivariate regularly varying random walks