Subexponential loss rate asymptotics for Lévy processes
نویسنده
چکیده
We consider a Lévy process reflected in barriers at 0 and K > 0. The loss rate is the mean time spent at the upper barrier K at time 1 when the process is started in stationarity, and is a natural continuous-time analogue of the stationary expected loss rate for a reflected random walk. We derive asymptotics for the loss rate when K tends to infinity, when the mean of the Lévy process is negative and the positive jumps are subexponential. In the course of this derivation, we achieve a formula, which is a generalization of the celebrated Pollaczeck-Khinchine formula.
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عنوان ژورنال:
- Math. Meth. of OR
دوره 73 شماره
صفحات -
تاریخ انتشار 2011