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 (Corresponding author), Jose Blanchet, Chang Han Rhee, Bert Zwart

Stochastic Operations Research

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

9 Citaten (Scopus)

36 Downloads (Pure)

Samenvatting

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.

Originele taal-2	Engels
Pagina's (van-tot)	2695-2739
Aantal pagina's	45
Tijdschrift	Annals of Applied Probability
Volume	30
Nummer van het tijdschrift	6
DOI's	https://doi.org/10.1214/20-AAP1570
Status	Gepubliceerd - dec. 2020

Bibliografische nota

Publisher Copyright:
© 2020 Institute of Mathematical Statistics.

Financiering

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.

Toegang tot document

10.1214/20-AAP1570

20-AAP1570Definitieve gepubliceerde versie, 471 KB

Andere bestanden en links

Link naar publicatie in Scopus

Citeer dit

@article{6d21df41b1ed44de991b42c6500b9c7c,

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",

volume = "30",

pages = "2695--2739",

journal = "Annals of Applied Probability",

issn = "1050-5164",

publisher = "Institute of Mathematical Statistics",

number = "6",

}

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

UR - http://www.scopus.com/inward/record.url?scp=85097686129&partnerID=8YFLogxK

U2 - 10.1214/20-AAP1570

DO - 10.1214/20-AAP1570

M3 - Article

AN - SCOPUS:85097686129

SN - 1050-5164

VL - 30

SP - 2695

EP - 2739

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

Samenvatting

Bibliografische nota

Financiering

Toegang tot document

Andere bestanden en links

Vingerafdruk

Citeer dit