A NOTE ON STABILITY OF THE SPLIT-STEP BACKWARD EULER METHOD FOR LINEAR STOCHASTIC DELAY INTEGRO-DIFFERENTIAL EQUATIONS∗

the split-step backward Euler (SSBE) method for linear stochastic delay integro-differential equations (SDIDEs) and proved the mean-square stability of SSBE method under some condition. Unfortu-nately, the main result of stability derived by the condition is somewhat restrictive to be applied for practical application. This paper improves the corresponding results. The authors not only prove the mean-square stability of the numerical method but also prove the general mean-square stability of the numerical method. Furthermore, an example is given to illustrate the theory. Key words General mean-square stability, mean-square stability, split-step backward Euler method, stochastic delay integro-differential equations.