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We propose an unconditionally convergent linear finite element scheme for thestochastic Landau--Lifshitz--Gilbert (LLG) equation with multi-dimensionalnoise. By using the Doss-Sussmann technique, we first transform the stochasticLLG equation into a partial differential equation that depends on the solutionof the auxiliary equation for the diffusion part. The resulting equation hassolutions absolutely continuous with respect to time. We then propose aconvergent $\theta$-linear scheme for the numerical solution of thereformulated equation. As a consequence, we are able to show the existence ofweak martingale solutions to the stochastic LLG equation.

A finite element approximation for the stochastic Landau--Lifshitz--Gilbert equation with multi-dimensional noise