Existence and linear approximation for the stochastic 3D magnetohydrodynamic-alpha model

We consider the 3D magnetohydrodynamic-alpha model driven by a multiplicative noise. The model arises in the modelling of turbulent flows in magneto fluids. We prove the existence and uniqueness of the probabilistic strong solution. We also propose and analyze a numerical scheme for the approximation of the unique strong solution. We prove the convergence in mean square of the scheme, which is a linear evolution equation with additive noise.