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

0451399 - ÚTIA 2016 RIV CZ eng J - Journal Article
Baňas, L. - Brzezniak, Z. - Neklyudov, M. - Ondreját, Martin - Prohl, A.
Ergodicity for a Stochastic Geodesic Equation in the Tangent Bundle of the 2D Sphere.
Czechoslovak Mathematical Journal. Roč. 65, č. 3 (2015), s. 617-657. ISSN 0011-4642. E-ISSN 1572-9141
R&D Projects: GA ČR GAP201/10/0752
Institutional support: RVO:67985556
Keywords : geometric stochastic wave equation * stochastic geodesic equation * ergodicity * attractivity * invariant measure * numerical approximation
Subject RIV: BA - General Mathematics
Impact factor: 0.284, year: 2015
http://library.utia.cas.cz/separaty/2015/SI/ondrejat-0451399.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0252658