Geodesic
Extensions of dynamical systems and martingale approximation method
Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part 13, Tome 216 (1994), pp. 10-19

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Let $T$ be a measure preserving transformation of a probability space $(\mathcal{X,F},\mu)$ and $A$ be the generator of a $\mu$-symmetric Markov process with state space $X$. Under assumption that $A$ is an “eigenvector” for $T$ an extension of $T$ is constructed in terms of $A$. By means of this extension a version of the central limit theorem is proved via approximation by martingales. Bibliography: 5 titles. 
@article{ZNSL_1994_216_a1,
     author = {M. I. Gordin},
     title = {Extensions of dynamical systems and martingale approximation method},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {10--19},
     publisher = {mathdoc},
     volume = {216},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_216_a1/}
}
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M. I. Gordin. Extensions of dynamical systems and martingale approximation method. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part 13, Tome 216 (1994), pp. 10-19. http://geodesic.mathdoc.fr/item/ZNSL_1994_216_a1/