LARGE DEVIATIONS OF INVARIANT MEASURES FOR DEGENERATE
DIFFUSIONS
Abstract: In this note we study large deviations of invariant measures for stable dynamical
systems under small noise perturbations of white noise type. The systems are modelled by
diffusion equations with a diffusion term
which we allow to be degenerated. The
corresponding invariant measures converge to a measure concentrated at the stable point and
their logarithms are compared with the optimal values of linear deterministic control
problems with quadratic functionals.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -