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Large deviations and stochastic flows of diffeomorphisms. (English) Zbl 0638.60035
Previous results in the theory of large deviations for additive functionals of a diffusion process on a compact manifold M are extended and then applied to the analysis of the Lyapunov exponents of a stochastic flow of diffeomorphisms of M. An approximation argument relates these results to the behavior near the diagonal \(\Delta\) in M 2 of the associated two-point motion.
Finally it is shown, under appropriate non-degeneracy conditions, that the two-point motion is ergodic on M 2-\(\Delta\) if the top Lyapunov exponent is positive.

MSC:
60F10 Large deviations
58J65 Diffusion processes and stochastic analysis on manifolds
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J60 Diffusion processes
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