We study sample-path large deviations for Ĺevy 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 nonexistence 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.
|Original language||English (US)|
|State||Published - Oct 11 2017|
- heavy tails
- random walks
- Sample path large deviations
- Ĺevy processes
ASJC Scopus subject areas