Weak convergence of the empirical process of intermittent maps in L-2 under long-range dependence
Taqqu, Murad S.
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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
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.