Convergence and stability of the semi-implicit Euler method for linear stochastic delay integro-differential equations

This paper deals with the convergence and stability of the semi-implicit Euler method for linear stochastic delay integro-differential equations. It is proved that the semi-implicit Euler method is convergent with strong order p = 0.5. The condition under which the method is asymptotic mean square stable is determined and numerical experiments are presented.