Well-posedness for the stochastic Landau–Lifshitz–Gilbert equation with helicity driven by jump noise

Soham Gokhale

Statistics & Probability Letters, 2025, vol. 216, issue C

Abstract: We consider the stochastic Landau–Lifshitz–Gilbert equation driven by pure jump noise. We assume non-zero contribution from the helicity term to the total energy. Using finite dimensional approximation followed by a generalization of the Jakubowski’s version of the Skorohod Theorem for non-metric spaces, we show that the considered problem admits a weak martingale solution. Restricting the problem to dimension 1, we show that the obtained solution is pathwise unique, thereby concluding the existence of a strong solution.

Keywords: Stochastic partial differential equations; Stochastic Landau–Lifshitz–Gilbert equation; Ferromagnetism; Helicity; Marcus Canonical form (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2024.110285

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