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2005 Sample Path Large Deviations Principles for Poisson Shot Noise Processes and Applications
Ayalvadi Ganesh, Claudio Macci, Giovanni Torrisi
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Electron. J. Probab. 10: 1026-1043 (2005). DOI: 10.1214/EJP.v10-273

Abstract

This paper concerns sample path large deviations for Poisson shot noise processes, and applications in queueing theory. We first show that, under an exponential tail condition, Poisson shot noise processes satisfy a sample path large deviations principle with respect to the topology of pointwise convergence. Under a stronger superexponential tail condition, we extend this result to the topology of uniform convergence. We also give applications of this result to determining the most likely path to overflow in a single server queue, and to finding tail asymptotics for the queue lengths at priority queues.

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Ayalvadi Ganesh. Claudio Macci. Giovanni Torrisi. "Sample Path Large Deviations Principles for Poisson Shot Noise Processes and Applications." Electron. J. Probab. 10 1026 - 1043, 2005. https://doi.org/10.1214/EJP.v10-273

Information

Accepted: 3 August 2005; Published: 2005
First available in Project Euclid: 1 June 2016

zbMATH: 1109.60017
MathSciNet: MR2164039
Digital Object Identifier: 10.1214/EJP.v10-273

Subjects:
Primary: 60F10
Secondary: 60F17, 60K25

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