  In this note we study the asymptotic mean-square stability for two-step
schemes applied to a scalar stochastic differential equation (sde) and applied
to systems of sdes. We derive necessary and sufficient conditions for the
asymptotic MS-stability of the methods in terms of the parameters of the
schemes. The stochastic Backward Differentiation Formula (BDF2) scheme is
asymptotically mean-square stable for any step-size whereas the two-step
Adams-Bashforth (AB2) and Adams-Moulton (AM2) methods are unconditionally
stable. The improved versions of the schemes do not perform better w.r.t their
stability behavior in the scalar case, as expected, but the situation is
different in more dimensions. Numerical experiments confirm theoretical
results.
