Summary
LetL(γ),γ≧0, γ≧0, denote the class of distributionsF satisfying
The classesL(γ), for γ>0, are characterized by means of subexponential densities. As an application we derive a result on the asymptotic behaviour of densities of random sums. In particular for anM/G/1 queue, we relate the tail behaviour of the stationary waiting time density to that of the service time distribution.
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Klüppelberg, C. Subexponential distributions and characterizations of related classes. Probab. Th. Rel. Fields 82, 259–269 (1989). https://doi.org/10.1007/BF00354763
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DOI: https://doi.org/10.1007/BF00354763