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

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JournalCzechoslovak Mathematical Journal
DatePublished - 2015
Issue number3
Volume65
Number of pages41
Pages (from-to)617-657
Original languageEnglish

Abstract

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 motivatea and illustrate the theoretical results.

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