Characterization of bistability for stochastic multistep methods

The focus of this article lies on the bistability of multistep methods applied to stochastic ordinary differential equations. Here bistability is understood in the sense of F. Stummel and leads to two-sided estimates of the strong error of convergence. It is shown that bistability can be characterized by Dahlquist’s strong root condition. The main ingredient of the stability analysis is a stochastic version of Spijker’s norm.