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Fluctuation theory in continuous time

Published online by Cambridge University Press:  01 July 2016

N. H. Bingham
N. H. Bingham*
Affiliation:
Westfield College, University of London
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Abstract

Our aim here is to give a survey of that part of continuous-time fluctuation theory which can be approached in terms of functionals of Lévy processes, our principal tools being Wiener-Hopf factorisation and local-time theory. Particular emphasis is given to one- and two-sided exit problems for spectrally negative and spectrally positive processes, and their applications to queues and dams. In addition, we give some weak-convergence theorems of heavy-traffic type, and some tail-estimates involving regular variation.

Keywords

LÉVY PROCESSWIENER-HOPF FACTORISATIONLOCAL TIMESUPREMUM FUNCTIONALSPECTRALLY NEGATIVESPECTRALLY POSITIVEM/G/1 QUEUEINFINITE DAMFINITE DAMHEAVY TRAFFIC

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Type
Research Article
Information
Advances in Applied Probability , Volume 7 , Issue 4 , December 1975 , pp. 705 - 766
Copyright
Copyright © Applied Probability Trust 1975 

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