Attractivity, invariance and ergodicity for SDEs on Riemannian manifolds
arXiv:1102.07282 citationsh-index: 34
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Theoretical advance for stochastic analysis on manifolds, but incremental as it extends known ergodicity results to a broader class of SDEs.
The paper provides a sufficient condition for SDEs on compact Riemannian manifolds ensuring weak convergence of solution laws to the normalized volume measure, and applies it to characterize invariant and ergodic measures.
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.