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- Title
On the infimum attained by a reflected Lévy process.
- Authors
Dębicki, K.; Kosiński, K.; Mandjes, M.
- Abstract
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) (for different classes of functions T and u large); here we have to distinguish between heavy-tailed and light-tailed scenarios.
- Subjects
LEVY processes; LAPLACE transformation; LARGE deviations (Mathematics); BROWNIAN motion; DISTRIBUTION (Probability theory)
- Publication
Queueing Systems, 2012, Vol 70, Issue 1, p23
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-011-9257-7