Attractivity, invariance and ergodicity for SDEs on Riemannian manifolds

Lubomir Banas; Zdzislaw Brzezniak; Martin Ondrejat; Andreas Prohl

doi:10.1007/s10587-015-0200-7

Attractivity, invariance and ergodicity for SDEs on Riemannian manifolds

Probability 2019-05-28 v1 Numerical Analysis

Authors: 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.

Keywords

stochastic differential equation riemannian manifold invariant measure ergodic measure weak convergence nonlinearity compact manifold

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@article{arxiv.1102.0728,
  title  = {Attractivity, invariance and ergodicity for SDEs on Riemannian manifolds},
  author = {Lubomir Banas and Zdzislaw Brzezniak and Martin Ondrejat and Andreas Prohl},
  journal= {arXiv preprint arXiv:1102.0728},
  year   = {2019}
}

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

Attractivity, invariance and ergodicity for SDEs on Riemannian manifolds

Abstract

Keywords

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