We introduce a new family of explicit integrators for stiff Itˆo stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of onestep stabilized methods with extended stability domains and do not suffer from stepsize reduction that standard explicit methods face. The family is based on the classical stabilized methods of order two for deterministic problems and its construction relies on the strategy of modified equations recently introduced for SDEs. The convergence and the stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations (SPDEs), are presented and confirm the theoretical results
