Attractivity, invariance and ergodicity for SDEs on Riemannian manifolds

Abstract

We give a sufficient condition on nonlinearities of an SDE on a compact connected Riemannian manifold $M$ which implies that laws of all solutions converge weakly to the normalized Riemannian volume measure on $M$. This result is further applied to characterize invariant and ergodic measures for various SDEs on manifolds.

arXiv commentfull preprint available at: http://na.uni-tuebingen.de/pub/prohl/papers/SDEs_Jan05.pdf