Article
MSC:
37A25,
58J65,
60H10,
60H15,
60H35,
60J60,
65C20,
65C30 | MR 3407597 | Zbl 06537684 | DOI: 10.1007/s10587-015-0200-7
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Keywords:
geometric stochastic wave equation; stochastic geodesic equation; ergodicity; attractivity; invariant measure; numerical approximation
geometric stochastic wave equation; stochastic geodesic equation; ergodicity; attractivity; invariant measure; numerical approximation
Summary:
We study ergodic properties of stochastic geometric wave equations on a particular model with the target being the 2D sphere 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. Studying this equation, we prove existence and non-uniqueness of invariant probability measures for the original problem and obtain also results on attractivity towards an invariant measure. We also present a structure-preserving numerical scheme to approximate solutions and provide computational experiments to motivate and illustrate the theoretical results.
References:
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