Sample path large deviations for Lévy processes and random walks with Weibull increments

Bazhba, Mihail; Blanchet, Jose; Rhee, Chang-Han; Zwart, Bert

doi:10.1214/20-AAP1570

M. Bazhba (Mihail), J. Blanchet (Jose), C.H. Rhee (Chang-Han) and A.P. Zwart (Bert)

2020-12-01

Sample path large deviations for Lévy processes and random walks with Weibull increments

Annals of Applied Probability , Volume 30 - Issue 6 p. 2695- 2739

We study sample path large deviations for Lévy processes and random walks with heavy-tailed jump-size distributions that are of Weibull type. The sharpness and applicability of these results are illustrated by a counterexample proving the nonexistence of a full LDP in the J1 topology, and by an application to a first passage problem.

Additional Metadata
Keywords	Heavy tails, Lévy processes, Random walks, Sample path large deviations
Persistent URL	doi.org/10.1214/20-AAP1570
Journal	Annals of Applied Probability
Project	Rare events: Asymptotics, Algorithms, Applications
Grant	This work was funded by the The Netherlands Organisation for Scientific Research (NWO); grant id nwo/639.033.413 - Rare events: Asymptotics, Algorithms, Applications
Organisation	Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands
Citation APA Style AAA Style APA Style Cell Style Chicago Style Harvard Style IEEE Style MLA Style Nature Style Vancouver Style American-Institute-of-Physics Style Council-of-Science-Editors Style BibTex Format Endnote Format RIS Format CSL Format DOIs only Format	Bazhba, M, Blanchet, J, Rhee, C.H, & Zwart, A.P. (2020). Sample path large deviations for Lévy processes and random walks with Weibull increments. Annals of Applied Probability, 30(6), 2695–2739. doi:10.1214/20-AAP1570

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