Linear mean-square stability properties of semi-implicit weak order 2.0 Taylor schemes for systems of stochastic differential equations

We consider the two-parameter family of semi-implicit weak second order Taylor schemes introduced by Milstein to investigate mean-square stability (MS-stability) properties of these schemes for systems of stochastic differential equations (SDEs). We obtain stability matrices and other conditions for the schemes to be MS-stable for normal and non-normal test systems. It is shown that for normal test systems the MS-stability conditions are similar to those of linear scalar test, reported by other authors, while for non-normal test systems this property is not necessarily valid any more. Some figures are included to illustrate the MS-stability properties of the schemes.