MS-Stability Of Numerical Methods Of Stochastic Differential Equations

Motivated by the theory of stochastic stabilization anddestabilization of Xuerong Mao, it is shown in this paper that any nonlinearsystem v?d,(0=/(^(0^)in，d>2can be destabilized by Stratonovich noiseif the dimension d之2.This paper provides results concerning the structure of stochasticperturbations that are known to stabilize or destabilize the solutions ofsystems of differential equations, develop two classes of test equations for thelinear stability analysis of numerical methods applied to systems of stochasticordinary differential equations of Stratonovich type. This paper concludes themean-square stability condition of Numerical methods of StochasticDifferential Equations,...