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

2 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

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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10.1214/20-AAP1570

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title = "Sample path large deviations for l{\'e}vy processes and random walks with weibull increments",

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.",

keywords = "Heavy tails, L{\'e}vy processes, Random walks, Sample path large deviations",

author = "Mihail Bazhba and Jose Blanchet and Rhee, {Chang Han} and Bert Zwart",

note = "Funding Information: 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. Publisher Copyright: {\textcopyright} 2020 Institute of Mathematical Statistics.",

year = "2020",

month = dec,

doi = "10.1214/20-AAP1570",

language = "English (US)",

volume = "30",

pages = "2695--2739",

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TY - JOUR

T1 - Sample path large deviations for lévy processes and random walks with weibull increments

AU - Bazhba, Mihail

AU - Blanchet, Jose

AU - Rhee, Chang Han

AU - Zwart, Bert

N1 - Funding Information: 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. Publisher Copyright: © 2020 Institute of Mathematical Statistics.

PY - 2020/12

Y1 - 2020/12

N2 - 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.

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.

KW - Heavy tails

KW - Lévy processes

KW - Random walks

KW - Sample path large deviations

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JO - Annals of Applied Probability

JF - Annals of Applied Probability

IS - 6

ER -

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

Abstract

Keywords

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