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    Weak convergence of the empirical process of intermittent maps in L-2 under long-range dependence

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    Date Issued
    2015-06-01
    Publisher Version
    10.1142/S0219493715500082
    Author(s)
    Dedecker, Jerome
    Dehling, Herold
    Taqqu, Murad S.
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    Permanent Link
    https://hdl.handle.net/2144/37505
    Version
    First author draft
    Citation (published version)
    Jerome Dedecker, Herold Dehling, Murad S Taqqu. 2015. "Weak convergence of the empirical process of intermittent maps in L-2 under long-range dependence." STOCHASTICS AND DYNAMICS, Volume 15, Issue 2, (29). https://doi.org/10.1142/S0219493715500082
    Abstract
    We study the behavior of the empirical distribution function of iterates of intermittent maps in the Hilbert space of square integrable 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.
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    • CAS: Mathematics & Statistics: Scholarly Papers [263]
    • BU Open Access Articles [3666]


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