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

Title:

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

Creator:

Baňas, Ľubomír, Brzeźniak, Zdzisłlaw, Neklyudov, Mikhail, Ondreját, Martin, and Prohl, Andreas

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:e9cabf7c-2a67-476c-a996-fc8976c24972
uuid:e9cabf7c-2a67-476c-a996-fc8976c24972
issn:0011-4642

Subject:

mathematics, geometric stochastic wave equation, stochastic geodesic equation, ergodicity, attractivity, invariant measure, numerical approximation, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

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., Ľubomír Baňas, Zdzisłlaw Brzeźniak, Mikhail Neklyudov, Martin Ondreját, Andreas Prohl., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

617-657

Source:

Czechoslovak Mathematical Journal | 2015 Volume:65 | Number:3

Harvested from:

CDK

Metadata only:

false