Random processes generated by a hyperbolic sequence of mappings. I

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.