Counting and convergence in ergodic theory
Idris Assani, Zoltán Buczolich, Daniel R. Mauldin (2004)
Acta Universitatis Carolinae. Mathematica et Physica
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Counting and convergence in ergodic theory
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The author investigates non ergodic versions of several well known limit theorems for strictly stationary processes. In some cases, the assumptions which are given with respect to general invariant measure, guarantee the validity of the theorem with respect to ergodic components of the measure. In other cases, the limit theorem can fail for all ergodic components, while for the original invariant measure it holds.