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. 
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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/

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