Sample path large deviations for lévy processes and random walks with weibull increments

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

doi:10.1214/20-AAP1570

Sample path large deviations for lévy processes and random walks with weibull increments

Mihail Bazhba, Jose Blanchet, Chang Han Rhee, Bert Zwart

Industrial Engineering and Management Sciences

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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 J1 topology, and by an application to a first passage problem.

Original language	English (US)
Pages (from-to)	2695-2739
Number of pages	45
Journal	Annals of Applied Probability
Volume	30
Issue number	6
DOIs	https://doi.org/10.1214/20-AAP1570
State	Published - Dec 2020

Funding

Acknowledgements. The research of BZ and MB is supported by NWO Grant 639.033.413. The research of JB is supported by NSF Grants 1915967, 1820942, 1838576 as well as DARPA Award N660011824028.

Keywords

Heavy tails
Lévy processes
Random walks
Sample path large deviations

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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abstract = "We study sample path large deviations for L{\'e}vy 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 J1 topology, and by an application to a first passage problem.",

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AU - Rhee, Chang Han

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AB - 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 J1 topology, and by an application to a first passage problem.

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Sample path large deviations for lévy processes and random walks with weibull increments

Abstract

Funding

Keywords

ASJC Scopus subject areas

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