  We study here the approximation by a finite-volume scheme of a heat equation
forced by a Lipschitz continuous multiplicative noise in the sense of It\^o.
More precisely, we consider a discretization which is semi-implicit in time and
a two-point flux approximation scheme (TPFA) in space. We adapt the method
based on the theorem of Prokhorov to obtain a convergence in distribution
result, then Skorokhod's representation theorem yields the convergence of the
scheme towards a martingale solution and the Gy\"{o}ngy-Krylov argument is used
to prove convergence in probability of the scheme towards the unique
variational solution of our parabolic problem.
