Work

Functional large deviations for multivariate regularly varying random walks

Year: 2005

Type: article

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 càdlàg 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.

Source: The Annals of Applied Probability

DOI: 10.1214/105051605000000502

Authors: Henrik Hult, Filip Lindskog, Thomas Mikosch, Gennady Samorodnitsky

Institutions: University of Copenhagen, Cornell University, KTH Royal Institute of Technology

Language: English

Topic: Probability and Risk Models

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: bronze

Funders: National Science Foundation, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Vetenskapsrådet, Swiss Re

Award: Theory and Applications of Heavy Tails and Long Range Dependence