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August 2012 Function-indexed empirical processes based on an infinite source Poisson transmission stream
François Roueff, Gennady Samorodnitsky, Philippe Soulier
Bernoulli 18(3): 783-802 (August 2012). DOI: 10.3150/11-BEJ367

Abstract

We study the asymptotic behavior of empirical processes generated by measurable bounded functions of an infinite source Poisson transmission process when the session length have infinite variance. In spite of the boundedness of the function, the normalized fluctuations of such an empirical process converge to a non-Gaussian stable process. This phenomenon can be viewed as caused by the long-range dependence in the transmission process. Completing previous results on the empirical mean of similar types of processes, our results on nonlinear bounded functions exhibit the influence of the limit transmission rate distribution at high session lengths on the asymptotic behavior of the empirical process. As an illustration, we apply the main result to estimation of the distribution function of the steady state value of the transmission process.

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François Roueff. Gennady Samorodnitsky. Philippe Soulier. "Function-indexed empirical processes based on an infinite source Poisson transmission stream." Bernoulli 18 (3) 783 - 802, August 2012. https://doi.org/10.3150/11-BEJ367

Information

Published: August 2012
First available in Project Euclid: 28 June 2012

zbMATH: 1259.60036
MathSciNet: MR2948901
Digital Object Identifier: 10.3150/11-BEJ367

Rights: Copyright © 2012 Bernoulli Society for Mathematical Statistics and Probability

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Vol.18 • No. 3 • August 2012
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