Tid: 25 oktober 1999 kl 1515-1700
Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!
Föredragshållare: Hanspeter Schmidli, Department of Theoretical Statistics, Aarhus University. Publikationslista (List of Publications)
Titel: Queueing and Risk models perturbed by Lévy processes
We consider a risk or a queueing model described by an ergodic stationary marked point process. The model is perturbed by a Lévy process with no downward jumps. We assume that the stationary marked point process and the perturbation process are independent. For finding the ruin probability or the steady state distribution of the workload one has to find the distribution of the maximum of the process, where in the queueing case the time has to be reverted. The (modified) ladder time is defined as the first time where an event of the marked point process leads to a new maximum. Processes of this type were first considered by Gerber(1970) and Dufresne and Gerber(1991). The marked point process was a compound Poisson process and the perturbation process was Brownian motion. They obtained a Pollaczek-Khintchine type formula for the maximum of the process, where the distributions involved have interpretations as (modified) ladder heights. Furrer(1998) proved the same formula in the case where the perturbation is a stable Lévy motion. He did, however, not obtain the interpretation as ladder heights. In this paper properties of the process until the first ladder height are studied. Results of Dufresne and Gerber(1991), Furrer(1998), Asmussen and Schmidt (1995) and Asmussen, Frey, Rolski and Schmidt (1995) are generalized.
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