Sample-path large deviations for L\'evy processes and random walks with Weibull increments

Mihail Bazhba; Jose Blanchet; Chang-Han Rhee; Bert Zwart

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arXiv · 1710.04013

Sample-path large deviations for L\'evy processes and random walks with Weibull increments

Mihail Bazhba·Jose Blanchet·Chang-Han Rhee·Bert Zwart

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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 $J_1$ topology, and a full LDP in the $M_1'$ 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 $J_1$ topology, and by an application to a first passage problem.

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BibTeX RIS

Mihail Bazhba, Jose Blanchet, Chang-Han Rhee, Bert Zwart. 2017-10-11. Sample-path large deviations for L\'evy processes and random walks with Weibull increments. https://arxiv.org/abs/1710.04013

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