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 journalArticlepeer-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 languageEnglish (US)
JournalUnknown Journal
StatePublished - Oct 11 2017
Externally publishedYes

Keywords

  • heavy tails
  • random walks
  • Sample path large deviations
  • Ĺevy processes

ASJC Scopus subject areas

  • General

Fingerprint Dive into the research topics of 'Sample-path large deviations for Ĺevy processes and random walks with Weibull increments'. Together they form a unique fingerprint.

Cite this