Bibliografie

Journal Article

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

Baňas L., Brzezniak Z., Neklyudov M., Ondreját Martin, Prohl A.

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

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

: 10.1007/s10587-015-0200-7

: 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