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

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Ergodicity for a Stochastic Geodesic Equation in the Tangent Bundle of the 2D Sphere. / Banas, Lubomír; Brzezniak, Zdzislaw; Neklyudov, Mikhail; Ondreját, Martin; Prohl, Andreas.

In: Czechoslovak Mathematical Journal, Vol. 65, No. 3, 2015, p. 617-657.

Research output: Contribution to journalArticlepeer-review

Harvard

Banas, L, Brzezniak, Z, Neklyudov, M, Ondreját, M & Prohl, A 2015, 'Ergodicity for a Stochastic Geodesic Equation in the Tangent Bundle of the 2D Sphere', Czechoslovak Mathematical Journal, vol. 65, no. 3, pp. 617-657. https://doi.org/10.1007/s10587-015-0200-7

APA

Banas, L., Brzezniak, Z., Neklyudov, M., Ondreját, 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. https://doi.org/10.1007/s10587-015-0200-7

Vancouver

Banas L, Brzezniak Z, Neklyudov M, Ondreját 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. https://doi.org/10.1007/s10587-015-0200-7

Author

Banas, Lubomír ; Brzezniak, Zdzislaw ; Neklyudov, Mikhail ; Ondreját, Martin ; Prohl, Andreas. / Ergodicity for a Stochastic Geodesic Equation in the Tangent Bundle of the 2D Sphere. In: Czechoslovak Mathematical Journal. 2015 ; Vol. 65, No. 3. pp. 617-657.

Bibtex - Download

@article{f0e8eead22ae4b9491d5dadc53a02771,
title = "Ergodicity for a Stochastic Geodesic Equation in the Tangent Bundle of the 2D Sphere",
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.",
author = "Lubom{\'i}r Banas and Zdzislaw Brzezniak and Mikhail Neklyudov and Martin Ondrej{\'a}t and Andreas Prohl",
year = "2015",
doi = "10.1007/s10587-015-0200-7",
language = "English",
volume = "65",
pages = "617--657",
journal = "Czechoslovak Mathematical Journal",
issn = "0011-4642",
publisher = "Springer",
number = "3",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Ergodicity for a Stochastic Geodesic Equation in the Tangent Bundle of the 2D Sphere

AU - Banas, Lubomír

AU - Brzezniak, Zdzislaw

AU - Neklyudov, Mikhail

AU - Ondreját, Martin

AU - Prohl, Andreas

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

U2 - 10.1007/s10587-015-0200-7

DO - 10.1007/s10587-015-0200-7

M3 - Article

VL - 65

SP - 617

EP - 657

JO - Czechoslovak Mathematical Journal

JF - Czechoslovak Mathematical Journal

SN - 0011-4642

IS - 3

ER -