Weak second order explicit stabilized methods for stiff stochastic differential equations, preprint submitted for publication

We introduce a new family of explicit integrators for stiff Ito ̂ stochastic differential equa-tions (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from the stepsize re-duction faced by standard explicit methods. The family is based on the standard second or-der orthogonal Runge-Kutta Chebyshev methods (ROCK2) for deterministic problems. The convergence, and the mean-square and asymptotic stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations are presented and confirm the theoretical results