Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere
Probability
2014-03-27 v1
Abstract
We study ergodic properties of stochastic geometric wave equations on a particular model with the target being the 2D sphere while considering the space variable-independent solutions only. 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 we obtain also results on attractivity towards an invariant measure. We also present a suitable numerical scheme for approximating the solutions subject to a sphere constraint.
Keywords
Cite
@article{arxiv.1403.6811,
title = {Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere},
author = {L'ubomír Banas and Zdzisław Brzeźniak and Misha Neklyudov and Martin Ondreját and Andreas Prohl},
journal= {arXiv preprint arXiv:1403.6811},
year = {2014}
}
Comments
arXiv admin note: text overlap with arXiv:1102.0728