0451399 20240103211311.620151201235959.9 000362883100004 84944062359 10.1007/s10587-015-0200-7 41 s. P cav_un_epca*02564820011-4642653 (2015)617-657Springer geometric stochastic wave equation stochastic geodesic equation ergodicity attractivity invariant measure numerical approximation cav_un_auth*0323271 Baňas L. DE 20 cav_un_auth*0202382 Brzezniak Z. GB 15 cav_un_auth*0323272 Neklyudov M. IT 10 cav_un_auth*0260292 Ondreját Martin Stochastická informatika Department of Stochastic Informatics SI SI UTIA-B Department of Stochastic Informatics K 35 Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0212864 Prohl A. DE 20 http://library.utia.cas.cz/separaty/2015/SI/ondrejat-0451399.pdf GAP201/10/0752 GA ČR cav_un_auth*0263519 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. 2016 BA 5 RVO:67985556 http://hdl.handle.net/11104/0252658 cav_un_auth*0323273 Universität Tübingen, Mathematisches Institut cav_un_auth*0323274 University of Pisa, Department of Mathematics cav_un_auth*0323275 University of York, Department of Mathematics cav_un_auth*0323276 Universität Bielefeld, Fakultät für Mathematik S MATHEMATICS 0.377 0.054 999.9 0.00172 0.281 922 0.374 Q3 0.252 74 Q4 18.91 5.9 Q4 Q3 5.929 2015 84944062359 SCOPUS 000362883100004 WOS cav_un_epca*0256482 Czechoslovak Mathematical Journal 0011-4642 1572-9141 Roč. 65 č. 3 2015 617 657 Springer