TY - JOUR

T1 - On the infimum attained by a reflected Lévy process

AU - Debicki, K.G.

AU - Kosinski, K.M.

AU - Mandjes, M.R.H.

PY - 2012

Y1 - 2012

N2 - 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(T u )>u) (for different classes of functions T u and u large); here we have to distinguish between heavy-tailed and light-tailed scenarios.

AB - 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(T u )>u) (for different classes of functions T u and u large); here we have to distinguish between heavy-tailed and light-tailed scenarios.

U2 - 10.1007/s11134-011-9257-7

DO - 10.1007/s11134-011-9257-7

M3 - Article

VL - 70

SP - 23

EP - 35

JO - Queueing Systems: Theory and Applications

JF - Queueing Systems: Theory and Applications

SN - 0257-0130

IS - 1

ER -