Sample Path Large Deviations Principles for Poisson Shot Noise Processes and Applications
Ayalvadi Ganesh, Microsoft Research
Claudio Macci, Universita degli Studi di Roma
Giovanni Luca Torrisi, Istituto per le Applicazioni del Calcolo
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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