Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere
Banas L, Brzezniak Z, Neklyudov M, Ondrejat M, Prohl A (2015)
Czechoslovak Mathematical Journal 65(3): 617-657.
Zeitschriftenaufsatz
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Autor*in
Banas, LubomirUniBi;
Brzezniak, Zdzislaw;
Neklyudov, Mikhail;
Ondrejat, Martin;
Prohl, Andreas
Einrichtung
Abstract / Bemerkung
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.
Stichworte
geometric stochastic wave equation;
ergodicity;
attractivity;
stochastic geodesic equation;
numerical approximation;
invariant measure
Erscheinungsjahr
2015
Zeitschriftentitel
Czechoslovak Mathematical Journal
Band
65
Ausgabe
3
Seite(n)
617-657
ISSN
0011-4642
Page URI
https://pub.uni-bielefeld.de/record/2786402
Zitieren
Banas L, Brzezniak Z, Neklyudov M, Ondrejat M, Prohl A. Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere. Czechoslovak Mathematical Journal. 2015;65(3):617-657.
Banas, L., Brzezniak, Z., Neklyudov, M., Ondrejat, M., & Prohl, A. (2015). Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere. Czechoslovak Mathematical Journal, 65(3), 617-657. doi:10.1007/s10587-015-0200-7
Banas, Lubomir, Brzezniak, Zdzislaw, Neklyudov, Mikhail, Ondrejat, Martin, and Prohl, Andreas. 2015. “Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere”. Czechoslovak Mathematical Journal 65 (3): 617-657.
Banas, L., Brzezniak, Z., Neklyudov, M., Ondrejat, M., and Prohl, A. (2015). Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere. Czechoslovak Mathematical Journal 65, 617-657.
Banas, L., et al., 2015. Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere. Czechoslovak Mathematical Journal, 65(3), p 617-657.
L. Banas, et al., “Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere”, Czechoslovak Mathematical Journal, vol. 65, 2015, pp. 617-657.
Banas, L., Brzezniak, Z., Neklyudov, M., Ondrejat, M., Prohl, A.: Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere. Czechoslovak Mathematical Journal. 65, 617-657 (2015).
Banas, Lubomir, Brzezniak, Zdzislaw, Neklyudov, Mikhail, Ondrejat, Martin, and Prohl, Andreas. “Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere”. Czechoslovak Mathematical Journal 65.3 (2015): 617-657.
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