Sample-path large deviations for L\'evy processes and random walks with Weibull increments
Probability
2019-12-06 v2
Abstract
We study sample-path large deviations for L\'evy 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 topology, and a full LDP in the topology. The rate function can be represented as the solution to a quasi-variational problem. The sharpness and applicability of these results are illustrated by a counterexample proving the nonexistence of a full LDP in the topology, and by an application to a first passage problem.
Cite
@article{arxiv.1710.04013,
title = {Sample-path large deviations for L\'evy processes and random walks with Weibull increments},
author = {Mihail Bazhba and Jose Blanchet and Chang-Han Rhee and Bert Zwart},
journal= {arXiv preprint arXiv:1710.04013},
year = {2019}
}