Geodesic
Random processes generated by a hyperbolic sequence of mappings. I
Izvestiya. Mathematics , Tome 44 (1995) no. 2, pp. 247-279

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For a sequence of smooth mappings of a Riemannian manifold, which is a nonstationary analogue of a hyperbolic dynamical system, a compatible sequence of measures carrying one into another under the mappings is constructed. A geometric interpretation is given for these measures, and it is proved that they depend smoothly on the parameter. The central limit theorem is proved for a sequence of smooth functions on the manifold with respect to these measures; it is shown that the correlations decrease exponentially, and an exponential estimate like Bernstein's inequality is obtained for probabilities of large deviations. 
@article{IM2_1995_44_2_a2,
     author = {V. I. Bakhtin},
     title = {Random processes generated by a hyperbolic sequence of mappings. {I}},
     journal = {Izvestiya. Mathematics },
     pages = {247--279},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1995_44_2_a2/}
}
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V. I. Bakhtin. Random processes generated by a hyperbolic sequence of mappings. I. Izvestiya. Mathematics , Tome 44 (1995) no. 2, pp. 247-279. http://geodesic.mathdoc.fr/item/IM2_1995_44_2_a2/