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arXiv · 1102.0728

Attractivity, invariance and ergodicity for SDEs on Riemannian manifolds

Lubomir Banas·Zdzislaw Brzezniak·Martin Ondrejat·Andreas Prohl
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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.

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Lubomir Banas, Zdzislaw Brzezniak, Martin Ondrejat, Andreas Prohl. 2011-02-03. Attractivity, invariance and ergodicity for SDEs on Riemannian manifolds. https://doi.org/10.1007/s10587-015-0200-7

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