Weak convergence of the empirical process of intermittent maps in L2 under long-range dependence

We study the behavior of the empirical distribution function of iterates of intermittent maps in the Hilbert space of square inegrable functions with respect to Lebesgue measure. In the long-range dependent case, we prove that the empirical distribution function, suitably normalized, converges to a...

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Published inarXiv.org
Main Authors Dedecker, Jérôme, Dehling, Herold G, Taqqu, Murad
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 22.11.2013
Subjects
Asymptotic methods
Convergence
Dependence
Distribution functions
Economic models
Hilbert space
Normal distribution
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Abstract We study the behavior of the empirical distribution function of iterates of intermittent maps in the Hilbert space of square inegrable functions with respect to Lebesgue measure. In the long-range dependent case, we prove that the empirical distribution function, suitably normalized, converges to a degenerate stable process, and we give the corresponding almost sure result. We apply the results to the convergence of the Wasserstein distance between the empirical measure and the invariant measure. We also apply it to obtain the asymptotic distribution of the corresponding Cramér-von-Mises statistic.
AbstractList We study the behavior of the empirical distribution function of iterates of intermittent maps in the Hilbert space of square inegrable functions with respect to Lebesgue measure. In the long-range dependent case, we prove that the empirical distribution function, suitably normalized, converges to a degenerate stable process, and we give the corresponding almost sure result. We apply the results to the convergence of the Wasserstein distance between the empirical measure and the invariant measure. We also apply it to obtain the asymptotic distribution of the corresponding Cramér-von-Mises statistic.
Author Dedecker, Jérôme
Taqqu, Murad
Dehling, Herold G
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SubjectTerms Asymptotic methods
Convergence
Dependence
Distribution functions
Economic models
Hilbert space
Normal distribution
Title Weak convergence of the empirical process of intermittent maps in L2 under long-range dependence
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