Convergence and stability of the split-step backward Euler method for linear stochastic delay integro-differential equations

In this paper, we focus on the numerical approximation of solutions of linear stochastic delay integro-differential equations (SDIDEs). Split-step backward Euler (SSBE) method for solving linear stochastic delay integro-differential equations is derived. It is proved that the SSBE method is convergent with strong order γ=12 in the mean-square sense. The condition under which the SSBE method is mean-square stable (MS-stable) is obtained. At last some scalar test equations are simulated. The numerical experiments verify the results obtained from theory.