Large Deviations and Stochastic Flows of Diffeomorphisms.

摘要

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-sq of the associated two points motion. Finally it is shown, under appropriate non-degeneracy conditions, that the two point motion is ergodic on M-sq-delta if the top Lyapunov exponent is positive. Reprints. (jhd)