Geodesic
On non-ergodic versions of limit theorems
Applications of Mathematics, Tome 34 (1989) no. 5, pp. 351-363.

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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.
DOI : 10.21136/AM.1989.104363
Classification : 28D05, 60B10, 60F05, 60F17, 60G10, 60G40
Keywords: central limit theorem for martingale differences; ergodic decomposition; invariance principle; invariant measure; law of iterated logarithm; strictly stationary sequence 
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     author = {Voln\'y, Dalibor},
     title = {On non-ergodic versions of limit theorems},
     journal = {Applications of Mathematics},
     pages = {351--363},
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     zbl = {0707.60027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1989.104363/}
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Volný, Dalibor. On non-ergodic versions of limit theorems. Applications of Mathematics, Tome 34 (1989) no. 5, pp. 351-363. doi : 10.21136/AM.1989.104363. http://geodesic.mathdoc.fr/articles/10.21136/AM.1989.104363/

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