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December 2020 Sample path large deviations for Lévy processes and random walks with Weibull increments
Mihail Bazhba, Jose Blanchet, Chang-Han Rhee, Bert Zwart
Ann. Appl. Probab. 30(6): 2695-2739 (December 2020). DOI: 10.1214/20-AAP1570

Abstract

We study sample path large deviations for Lévy processes and random walks with heavy-tailed jump-size distributions that are of Weibull type. 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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Mihail Bazhba. Jose Blanchet. Chang-Han Rhee. Bert Zwart. "Sample path large deviations for Lévy processes and random walks with Weibull increments." Ann. Appl. Probab. 30 (6) 2695 - 2739, December 2020. https://doi.org/10.1214/20-AAP1570

Information

Received: 1 November 2017; Revised: 1 November 2019; Published: December 2020
First available in Project Euclid: 14 December 2020

Digital Object Identifier: 10.1214/20-AAP1570

Subjects:
Primary: 60F10
Secondary: 60G17

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.30 • No. 6 • December 2020
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