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Subexponential loss rate asymptotics for Lévy processes

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Subexponential loss rate asymptotics for Lévy processes. / Andersen, Lars Nørvang.

I: Mathematical Methods of Operations Research, Bind 73, Nr. 1, 2011, s. 91-108.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

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Andersen, LN 2011, 'Subexponential loss rate asymptotics for Lévy processes', Mathematical Methods of Operations Research, bind 73, nr. 1, s. 91-108. https://doi.org/10.1007/s00186-010-0335-0

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Andersen, Lars Nørvang. / Subexponential loss rate asymptotics for Lévy processes. I: Mathematical Methods of Operations Research. 2011 ; Bind 73, Nr. 1. s. 91-108.

Bibtex

@article{52071d994dfe48da928ce8621ab4291c,
title = "Subexponential loss rate asymptotics for L{\'e}vy processes",
abstract = "We consider a L{\'e}vy process reflected in barriers at 0 and K > 0. The loss rate is the mean of the local time at K at time 1 when the process is started in stationarity, and is a natural continuous-time analogue of the stationary expected loss rate for a reflected random walk. We derive asymptotics for the loss rate when K tends to infinity, when the mean of the L{\'e}vy process is negative and the positive jumps are subexponential. In the course of this derivation, we achieve a formula, which is a generalization of the celebrated Pollaczeck-Khinchine formula. ",
author = "Andersen, {Lars N{\o}rvang}",
year = "2011",
doi = "10.1007/s00186-010-0335-0",
language = "English",
volume = "73",
pages = "91--108",
journal = "Mathematical Methods of Operations Research",
issn = "1432-2994",
publisher = "Springer",
number = "1",

}

RIS

TY - JOUR

T1 - Subexponential loss rate asymptotics for Lévy processes

AU - Andersen, Lars Nørvang

PY - 2011

Y1 - 2011

N2 - We consider a Lévy process reflected in barriers at 0 and K > 0. The loss rate is the mean of the local time at K at time 1 when the process is started in stationarity, and is a natural continuous-time analogue of the stationary expected loss rate for a reflected random walk. We derive asymptotics for the loss rate when K tends to infinity, when the mean of the Lévy process is negative and the positive jumps are subexponential. In the course of this derivation, we achieve a formula, which is a generalization of the celebrated Pollaczeck-Khinchine formula.

AB - We consider a Lévy process reflected in barriers at 0 and K > 0. The loss rate is the mean of the local time at K at time 1 when the process is started in stationarity, and is a natural continuous-time analogue of the stationary expected loss rate for a reflected random walk. We derive asymptotics for the loss rate when K tends to infinity, when the mean of the Lévy process is negative and the positive jumps are subexponential. In the course of this derivation, we achieve a formula, which is a generalization of the celebrated Pollaczeck-Khinchine formula.

U2 - 10.1007/s00186-010-0335-0

DO - 10.1007/s00186-010-0335-0

M3 - Journal article

VL - 73

SP - 91

EP - 108

JO - Mathematical Methods of Operations Research

JF - Mathematical Methods of Operations Research

SN - 1432-2994

IS - 1

ER -