We study sample-path large deviations for Lévy processes and random walks with heavy-tailed jump-size distributions that are of Weibull type. Our main results include an extended form of an LDP (large deviations principle) in the J1 topology, and a full LDP in the M′1 topology. The rate function can be represented as the solution of a quasi-variational problem. The sharpness and applicability of these results are illustrated by a counterexample proving non-existence of a full LDP in the J1 topology, and an application to the buildup of a large queue length in a queue with multiple servers.
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Keywords Sample path large deviations, Lévy processes, Random walks, Heavy tails
Citation
Bazhba, M, Blanchet, J, Rhee, C.H, & Zwart, A.P. (2017). Sample-path large deviations for Lévy processes and random walks with Weibull increments.