Weak Solutions of a Stochastic Landau–Lifshitz–Gilbert Equation Driven by Pure Jump Noise

Abstract

In this work we study a stochastic three-dimensional Landau–Lifshitz–Gilbert equation perturbed by pure jump noise in the Marcus canonical form. We show the existence of a weak martingale solution taking values in a two-dimensional sphere $${\mathbb{S}^2}$$ and discuss certain regularity results. The construction of a solution is based on the classical Faedo–Galerkin approximation, the compactness methods and the Jakubowski version of the Skorokhod Theorem for nonmetric spaces.