SAMPLE PATH LARGE DEVIATIONS FOR LÉVY PROCESSES AND RANDOM WALKS WITH WEIBULL INCREMENTS

SAMPLE PATH LARGE DEVIATIONS FOR LÉVY PROCESSES AND RANDOM WALKS WITH WEIBULL INCREMENTS

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 appl...

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Veröffentlicht in:The Annals of applied probability 2020-12, Vol.30 (6), p.2695-2739
Hauptverfasser: Bazhba, Mihail, Blanchet, Jose, Rhee, Chang-Han, Zwart, Bert
Format: Artikel
Sprache:eng
Schlagworte:
Deviation
Random walk
Random walk theory
Sharpness
Stochastic models
Topology
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Zusammenfassung: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.
ISSN:1050-5164
2168-8737
DOI:10.1214/20-AAP1570