A pathwise stochastic Landau-Lifshitz-Gilbert equation with application to large deviations

Gussetti E, Hocquet A (2023)
Journal of Functional Analysis 285(9): 110094.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Gussetti, EmanuelaUniBi ; Hocquet, Antoine
Abstract / Bemerkung
Using a rough path formulation, we investigate existence, uniqueness and regularity for the stochastic Landau-Lifshitz-Gilb ert equation with Stratonovich noise on the one dimensional torus. As a main result we show the continuity of the so-called Ito-Lyons map in the energy spaces L & INFIN;(0, T; Hk) & AND; L2(0, T; Hk+1) for any k & GE; 1. The proof proceeds in two steps. First, based on an energy estimate in the aforementioned space together with a compactness argument we prove existence of a unique solution, implying the continuous dependence in a weaker norm. This is then strengthened in the second step where the continuity in the optimal norm is established through an application of the rough Gronwall lemma. Our approach is direct and does not rely on any transformation formula, which permits to treat multidimensional noise. As an easy consequence we then deduce a Wong-Zakai type result, a large deviation principle for the solution and a sup-port theorem.& COPY; 2023 Elsevier Inc. All rights reserved.
Erscheinungsjahr
2023
Zeitschriftentitel
Journal of Functional Analysis
Band
285
Ausgabe
9
Art.-Nr.
110094
ISSN
0022-1236
eISSN
1096-0783
Page URI
https://pub.uni-bielefeld.de/record/2977913

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Gussetti E, Hocquet A. A pathwise stochastic Landau-Lifshitz-Gilbert equation with application to large deviations. Journal of Functional Analysis. 2023;285(9): 110094.
Gussetti, E., & Hocquet, A. (2023). A pathwise stochastic Landau-Lifshitz-Gilbert equation with application to large deviations. Journal of Functional Analysis, 285(9), 110094. https://doi.org/10.1016/j.jfa.2023.110094
Gussetti, Emanuela, and Hocquet, Antoine. 2023. “A pathwise stochastic Landau-Lifshitz-Gilbert equation with application to large deviations”. Journal of Functional Analysis 285 (9): 110094.
Gussetti, E., and Hocquet, A. (2023). A pathwise stochastic Landau-Lifshitz-Gilbert equation with application to large deviations. Journal of Functional Analysis 285:110094.
Gussetti, E., & Hocquet, A., 2023. A pathwise stochastic Landau-Lifshitz-Gilbert equation with application to large deviations. Journal of Functional Analysis, 285(9): 110094.
E. Gussetti and A. Hocquet, “A pathwise stochastic Landau-Lifshitz-Gilbert equation with application to large deviations”, Journal of Functional Analysis, vol. 285, 2023, : 110094.
Gussetti, E., Hocquet, A.: A pathwise stochastic Landau-Lifshitz-Gilbert equation with application to large deviations. Journal of Functional Analysis. 285, : 110094 (2023).
Gussetti, Emanuela, and Hocquet, Antoine. “A pathwise stochastic Landau-Lifshitz-Gilbert equation with application to large deviations”. Journal of Functional Analysis 285.9 (2023): 110094.

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Preprint: 10.48550/ARXIV.2103.00926

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