Loss Rate Asymptotics for Random Walks with Two Reflecting Barriers

Mats Pihlsgård

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2003

ISSN 1403-9338

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Abstract:

We consider the stationary loss rate l^K of a random walk reflected at 0 and some level K>0. We derive sharp asymptotics for the loss rate in non-lattice random walks with negative drift. As an

example, we consider the PH/PH/1 case, where we compare the exact loss rate to the asymptotic one and illustrate our results graphically with the help of a small MATLAB program.

Key words:

stationary loss rate, asymptotics, random walk, Lundberg's equation, Lundberg's inequality, Cram\'er--Lundberg approximation, phase--type distributions