Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere

Czechoslovak Mathematical Journal

Andreas Prohl⁷  ubomír Baňas^1,12  Mikhail Neklyudov^1,15  Martin Ondreját^1,16  Zdzisaw Brzeźniak^1,18 

[1] , Department of Mathematics, The University of York, Heslington, York YO10 5DD, United Kingdom,;, Department of Mathematics, University of Pisa, Largo Bruno Pontecorvo , Mathematisches Institut, Universitä, The Institute of Information Theory and Automation of the Czech Academy of Sciences, Pod Vodárenskou věží 08 Praha 10, 72076 Tü131, 33501 Bielefeld, Germany,;4, 182 5, Pisa 56127, Italy,;8, Czech Republic,;Fakultäbingen, Auf der Morgenstelle bingen, Germany;r Mathematik, Universität Bielefeld, Postfach 100 t Tüt fü

关键词: geometric stochastic wave equation;    stochastic geodesic equation;    ergodicity;    attractivity;    invariant measure;    numerical approximation;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

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.

【 授权许可】

Unknown