We consider stochastic perturbations of geodesic flow for left-invariant metrics on finite-dimensional Lie groups and study the Hörmander condition and some properties of the solutions of the corresponding Fokker–Planck equations.
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Acknowledgements We thank Jonathan Mattingly for an illuminating discussion. We also thank the referees for their very helpful comments, which were important for improving the original version of the article. The research was supported in part by Grants DMS 1362467 and DMS 1159376 from the National Science Foundation.
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- Left-invariant metrics
- Lie groups
- Stochastic perturbations