Discretization of a distributed control problem with a stochastic parabolic equation driven by multiplicative noise

A discretization of an optimal control problem of a stochastic parabolic equation driven by multiplicative noise is analyzed. The state equation is discretized by the continuous piecewise linear element method in space and by the backward Euler scheme in time. The convergence rate $ O(\tau^{1/2} + h^2) $ is rigorously derived.