Function-indexed empirical processes based on an infinite source Poisson transmission stream - Mathematics > ProbabilityReportar como inadecuado




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Abstract: We study the asymptotic behavior of empirical processes generated bymeasurable bounded functions of an infinite source Poisson transmission processwhen the session length have infinite variance. In spite of the boundedness ofthe function, the normalized fluctuations of such an empirical process convergeto a non-Gaussian stable process. This phenomenon can be viewed as caused bythe long-range dependence in the transmission process. Completing previousresults on the empirical mean of similar types of processes, our results onnon-linear bounded functions exhibit the influence of the limit transmissionrate distribution at high session lengths on the asymptotic behavior of theempirical process. As an illustration, we apply the main result to estimationof the distribution function of the steady state value of the transmissionprocess.



Autor: François Roueff LTCI, Gennady Samorodnitsky, Philippe Soulier MODAL'X

Fuente: https://arxiv.org/







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