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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.

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