2017-10-11
Sample-path large deviations for Lévy processes and random walks with Weibull increments
Publication
Publication
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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Organisation | Stochastics |
Bazhba, M., Blanchet, J., Rhee, C.-H., & Zwart, B. (2017). Sample-path large deviations for Lévy processes and random walks with Weibull increments. |