Explicit Stabilised Methods: Stochastic Differential Equations

This lecture discusses explicit stabilized methods for stiff Ito stochastic differential equations, introducing a new family of integrators with extended stability domains. The methods are analyzed for convergence, mean square, and asymptotic stability properties, with applications to nonlinear SDEs and parabolic SPDEs. The lecture also covers weak convergence, modified equations, backward error analysis, and invariant preserving integrators. Various numerical experiments confirm the theoretical findings and demonstrate the versatility of the methodology.