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