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.

Heavy tails, Lévy processes, Random walks, Sample path large deviations
doi.org/10.1214/20-AAP1570
Annals of Applied Probability
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

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