# Bibliography

Journal Article

### Ergodicity for a Stochastic Geodesic Equation in the Tangent Bundle of the 2D Sphere

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**: **Czechoslovak Mathematical Journal vol.65, 3 (2015), p. 617-657

**: **GAP201/10/0752, GA ČR

**: **geometric stochastic wave equation,
stochastic geodesic equation,
ergodicity,
attractivity,
invariant measure,
numerical approximation

**: **http://library.utia.cas.cz/separaty/2015/SI/ondrejat-0451399.pdf

**(eng): **Ergodic properties of stochastic geometric wave equations on a particular model with the target being the 2D sphere are studied while considering only solutions which are independent of the space variable. This simplification leads to a degenerate stochastic equation in the tangent bundle of the 2D sphere. Existence and non-uniqueness of invariant probability measures for the original problem are proved and results on attractivity towards an invariant measure are obtained. A structure-preserving numerical scheme to approximate solutions are presented and computational experiments to motivate and illustrate the theoretical results are provided.

**: **BA