Analysis of a splitting scheme for a class of nonlinear stochastic Schr\uf6dinger equations

We analyze the qualitative properties and the order of convergence of a splitting scheme for a class of nonlinear stochastic Schr\uf6dinger equations driven by additive It\uf4 noise. The class of nonlinearities of interest includes nonlocal interaction cubic nonlinearities. We show that the numerical solution is symplectic and preserves the expected mass for all times. On top of that, for the convergence analysis, some exponential moment bounds for the exact and numerical solutions are proved. This enables us to provide strong orders of convergence as well as orders of convergence in probability and almost surely. Finally, extensive numerical experiments illustrate the performance of the proposed numerical scheme

Convergence rates of the splitting scheme for parabolic linear stochastic Cauchy problems

We study the splitting scheme associated with the linear stochasti