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Limiting properties of Poisson shot noise processes

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Robert Lund ,
William P. McCormick  and
Yuanhui Xiao
Robert Lund*
Affiliation:
University of Georgia
William P. McCormick*
Affiliation:
University of Georgia
Yuanhui Xiao*
Affiliation:
University of Rochester
*
∗ Postal address: Department of Statistics, University of Georgia, Athens, GA 30602-1952, USA
∗ Postal address: Department of Statistics, University of Georgia, Athens, GA 30602-1952, USA
∗ Postal address: Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY 14642, USA
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Abstract

This paper studies limiting properties of discretely sampled Poisson shot noise processes. Versions of the law of large numbers and central limit theorem are derived under very general conditions. Examples demonstrating the utility of the results are included.

Keywords

Central limit theoremcompound Poisson processimpulse responselaw of large numbersshot noise

MSC classification

Primary: 60G25: Prediction theory
Secondary: 60G20: Generalized stochastic processes
Type
Short Communications
Information
Journal of Applied Probability , Volume 41 , Issue 3 , September 2004 , pp. 911 - 918
Copyright
Copyright © Applied Probability Trust 2004 

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