Abstract
We show that distributional and weak functional limit theorems for ergodic processes often hold for arbitrary absolutely continuous initial distributions. This principle is illustrated in the setup of ergodic sums, renewal-theoretic variables, and hitting times for ergodic measure preserving transformations.
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Zweimüller, R. Mixing Limit Theorems for Ergodic Transformations. J Theor Probab 20, 1059–1071 (2007). https://doi.org/10.1007/s10959-007-0085-y
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DOI: https://doi.org/10.1007/s10959-007-0085-y