Sample-path large deviations for Ĺevy processes and random walks with Weibull increments

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

Sample-path large deviations for Ĺevy processes and random walks with Weibull increments

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

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

Abstract

We study sample-path large deviations for Ĺevy processes and random walks with heavy-Tailed jump-size distributions that are of Weibull type. Our main results include an extended form of an LDP (large deviations principle) in the J1 topology, and a full LDP in the M 1 topology. The rate function can be represented as the solution of a quasi-variational problem. The sharpness and applicability of these results are illustrated by a counterexample proving nonexistence of a full LDP in the J1 topology, and an application to the buildup of a large queue length in a queue with multiple servers.

Original language	English (US)
Journal	Unknown Journal
State	Published - Oct 11 2017
Externally published	Yes

Keywords

heavy tails
random walks
Sample path large deviations
Ĺevy processes

ASJC Scopus subject areas

General

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title = "Sample-path large deviations for {\'L}evy processes and random walks with Weibull increments",

abstract = "We study sample-path large deviations for {\'L}evy processes and random walks with heavy-Tailed jump-size distributions that are of Weibull type. Our main results include an extended form of an LDP (large deviations principle) in the J1 topology, and a full LDP in the M 1 topology. The rate function can be represented as the solution of a quasi-variational problem. The sharpness and applicability of these results are illustrated by a counterexample proving nonexistence of a full LDP in the J1 topology, and an application to the buildup of a large queue length in a queue with multiple servers.",

keywords = "heavy tails, random walks, Sample path large deviations, {\'L}evy processes",

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

year = "2017",

month = oct,

day = "11",

language = "English (US)",

journal = "Free Radical Biology and Medicine",

issn = "0891-5849",

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T1 - Sample-path large deviations for Ĺevy processes and random walks with Weibull increments

AU - Bazhba, Mihail

AU - Blanchet, Jose

AU - Rhee, Chang Han

AU - Zwart, Bert

PY - 2017/10/11

Y1 - 2017/10/11

N2 - We study sample-path large deviations for Ĺevy processes and random walks with heavy-Tailed jump-size distributions that are of Weibull type. Our main results include an extended form of an LDP (large deviations principle) in the J1 topology, and a full LDP in the M 1 topology. The rate function can be represented as the solution of a quasi-variational problem. The sharpness and applicability of these results are illustrated by a counterexample proving nonexistence of a full LDP in the J1 topology, and an application to the buildup of a large queue length in a queue with multiple servers.

AB - We study sample-path large deviations for Ĺevy processes and random walks with heavy-Tailed jump-size distributions that are of Weibull type. Our main results include an extended form of an LDP (large deviations principle) in the J1 topology, and a full LDP in the M 1 topology. The rate function can be represented as the solution of a quasi-variational problem. The sharpness and applicability of these results are illustrated by a counterexample proving nonexistence of a full LDP in the J1 topology, and an application to the buildup of a large queue length in a queue with multiple servers.

KW - heavy tails

KW - random walks

KW - Sample path large deviations

KW - Ĺevy processes

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AN - SCOPUS:85093052180

JO - Free Radical Biology and Medicine

JF - Free Radical Biology and Medicine

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