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Sample Path Large Deviations of Poisson Shot Noise with Heavy-Tailed Semiexponential Distributions

Part of: Limit theorems

Published online by Cambridge University Press:  14 July 2016

Ken R. Duffy  and
Giovanni Luca Torrisi
Ken R. Duffy*
Affiliation:
National University of Ireland, Maynooth
Giovanni Luca Torrisi*
Affiliation:
Istituto per le Applicazioni del Calcolo
*
∗ Postal address: Hamilton Institute, National University of Ireland, Maynooth, Maynooth Co. Kildare, Ireland. Email address: ken.duffy@nuim.ie
∗∗ Postal address: Istituto per le Applicazioni del Calcolo ‘Mauro Picone’ (IAC-CNR), Via dei Taurini 19, I-00185 Roma, Italia. Email address: torrisi@iac.rm.cnr.it
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Abstract

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It is shown that the sample paths of Poisson shot noise with heavy-tailed semiexponential distributions satisfy a large deviation principle with a rate function that is insensitive to the shot shape. This demonstrates that, on the scale of large deviations, paths to rare events do not depend on the shot shape.

Keywords

Heavy-tailed distributionsample path large deviationPoisson shot noise

MSC classification

Secondary: 60F10: Large deviations
Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 3 , September 2011 , pp. 688 - 698
Copyright
Copyright © Applied Probability Trust 2011 

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