Speed of convergence to the quasi-stationary distribution for Lévy input fluid queues

Abstract

In this note we prove that the speed of convergence of the workload of a Lévy-driven queue to the quasi-stationary distribution is of order $1/t$. We identify also the Laplace transform of the measure giving this speed and provide some examples.

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• Population processes with unbounded extinction rate conditioned to non-extinction
• Yaglom limits can depend on the starting state