On the infimum attained by a reflected Lévy process

K.G. Debicki, K.M. Kosinski, M.R.H. Mandjes

Onderzoeksoutput: Boek/rapportRapportAcademic

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Samenvatting

This paper considers a Lévy-driven queue (i.e., a Lévy process reflected at 0), and focuses on the distribution of M(t), that is, the minimal value attained in an interval of length t (where it is assumed that the queue is in stationarity at the beginning of the interval). The first contribution is an explicit characterization of this distribution, in terms of Laplace transforms, for spectrally one-sided Lévy processes (i.e., either only positive jumps or only negative jumps). The second contribution concerns the asymptotics of P (M(Tu) > u) (for different classes of functions Tu and u large); here we have to distinguish between heavy-tailed and light-tailed scenarios.
Originele taal-2Engels
Plaats van productieEindhoven
UitgeverijEurandom
Aantal pagina's9
StatusGepubliceerd - 2011

Publicatie series

NaamReport Eurandom
Volume2011005
ISSN van geprinte versie1389-2355

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