A mass-preserving splitting scheme for the stochastic Schrodinger equation with multiplicative noise

We present a mass-preserving scheme for the stochastic nonlinear Schrodinger equation with multiplicative noise of Stratonovich type. It is a splitting scheme and we present an explicit formula for solving the sub-step related to the nonlinear part. The scheme is unconditionally stable in the L-2 norm. For the linear stochastic Schrodinger equation, we prove that the scheme has a strong convergence rate in time equal to 1, which is not common for stochastic partial differential equations with noise depending on space and time.