Attractivity, invariance and ergodicity for SDEs on Riemannian manifolds

Details Attractivity, invariance and ergodicity for SDEs on Riemannian manifolds Attractivity, invariance and ergodicity for SDEs on Riemannian manifolds

2011-02-03

arxiv.org/abs/1102.0728v1

Mathematics

Probability

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

Scientific paper

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.

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