A numerical method for a class of Itô stochastic differential equations with a finite delay term is introduced. The method is based on the forward Euler approximation and is parameterised by its time step. Weak convergence with respect to a class of smooth test functionals is established by...

A linear differential equation with infinite delay is considered in the generalized form as an integral equation. As usually, the function space ß of the admissible initial conditions is only described axiomatically. Merely using this abstract description the long time behavior of the solutions...

Numerical solutions of SDDE often reflect to only a limited extent the exact solution behaviour. Hence it is necessary to identify those parameters of SDDE and algorithm for which a numerical method in use is reliable. For affine SDDE test equations, there exist estimates of the stability...

The paper considers the derivation of weak discrete time approximations for solutions of stochastic differential equations with time delay. These are suitable for Monte Carlo simulation and allow the computation of expectations for functionals of stochastic delay equations. The suggested...